If we don’t turn a blind eye to the truth and be realistic, we will see that the perfection of the woman doesn’t lie in her having a status like that of men, and that it is also wrong for men to take pride in their gender.
The truth of the matter is that the creation of the human circles around two separate but harmonious halves, the man and the woman.
What brings superiority for both men and women are endeavors for achieving humanity, and in other words, using the potential placed in all of us for the best. Except for differences that are necessitated by the order of creation, there is no difference between the two genders from the Quran and revelation’s perspective.
Since this question is about the status of the woman in Islam, it is necessary to refer to Islamic sources, meaning the Quran and the traditions of the prophet (pbuh) and Ahlul-Bayt, to see what Islam’s view is on the issue.
The different dimensions of the woman’s status
The woman’s status in Islam can be looked at from three perspectives:
a) Her character
1- The woman is a symbol of elegance, tranquility and beauty. Every single thing in this universe is the manifestation of the attributes and names of Allah (swt), because creating which is one of His attributes of action (not one of the attributes of essence) is the manifestation of the creator in His different creations, as Imam Ali (as) puts it: “All praise is due to Allah (swt) who showed Himself to His creations through His creation.”  and 
from the Quran’s perspective, the secret behind creating the woman and establishing the base of the family and the union of marriage is higher than just lust and fulfilling desires and achieving temporary pleasures.
“And of His signs is that He created for you mates from your own selves that you may take comfort in them, and He ordained affection and mercy between you. There are indeed signs in that for a people who reflect” 
2- All racial, gender related, etc. advantages are vain, and “Indeed the noblest of you in the sight of Allah is the most God wary among you” 
3- All heavenly books and prophets have addressed humanity and not a specific gender saying: “Whosoever follows me indeed belongs to me” 
4- The status of the woman has no boundaries; she can succeed, possess and reach anything she desires: “O man! You are laboring toward your Lord laboriously, and you will encounter Him”  , “Every person is in custody of his own doings”  , “And that man can only have the fruit of what he has strived for; verily, the result of his effort will soon Be observed”  .
5- Whosoever serves Allah (swt) will be close to Him, regardless of whether it is a man or woman. “When My servants ask you about Me, [tell them that) I am indeed close. I answer the supplicant's call when he calls Me. So let them respond to Me, and let them have faith in Me, so that they may fare rightly.” 
6- In order to reach the tayyeb life (good and pure life), two conditions must be fulfilled: “Whoever acts righteously, [whether] male or female, should he be faithful, We shall revive him with a good life and pay them their reward by the best of what they used to do” 
7- Whosoever disregards the truth, will be cursed by Allah (swt): “Indeed those who turn faithless and die while they are faithless, it is they on whom shall be the curse of Allah, the angels and all mankind”. 
What is easily concluded from these verses is that the human is their addressee, not a specific gender. Humans are “hostages” of their faith and actions and they “pick the fruit of whatever they themselves plant”, let them be men or women. In revelation’s sight, the woman is a human and gender has no effect on the fundamentals of the obligations and character of people.
And now for the second dimension of the status of the woman in Islam:
b) The woman and the “ladder” of knowledge and nearness to Allah (swt)
1- Allah (swt) doesn’t exclusively belong to men nor women and the same goes for knowledge and getting closer to Him. There is a general formula that if one goes by, he/she will indeed achieve such a goal, and that formula is: knowledge, affection, obedience and nearness.
It doesn’t make a difference who and how much one goes after knowledge and wisdom, what is important is guidance and it is after guidance that this verse applies to us:
“Those who strive in our way, we will guide them to ways of nearness to Allah (swt)”; many have done so, men and women, and the Quran gives two examples of those who went this way and two examples of those who went the opposite:
“Allah draws an [other] example for those who have faith: the wife of Pharaoh, when she said," My Lord! Build me a home near You in paradise, and deliver me from Pharaoh and his conduct, and deliver me from the wrongdoing lot”  In the next verse, Allah (swt) gives the second example of a good character, which is Lady Maryam.
Also, the two bad people the Quran speaks of are also women (Prophet Nuh and Prophet Lut’s (pbuh) wives).  These good and bad women are examples for all, not just for women!
2- The most important requisite for getting closer to Allah (swt) is the heart and a broken heart, and women bear it more than men: “The ways to ascend and go higher for people varies. One way is through dhikr (invocation) and another is through thought; if women aren't higher and more successful than men in the first, which is the way of the heart and love and affection, they are certainly equal to them.” 
3- The holy prophet of Islam (pbuh) says: “The best knowledge is tawhid, and the best worship is istighfar (asking for repentance).”  Clearly, there is no difference between men and women in reaching such knowledge.
4- If we are pious and wary of Allah (swt), we will reach spirituality, and piety and taqwa don’t belong to a specific gender and group.
“Indeed if one is God wary and patient Allah does not waste the reward of the virtuous” 
“But as for him who is awed to stand before his Lord and forbids the soul from [following] desire,
his refuge will indeed be paradise” 
To make it short, different women who had reached very high levels of spirituality in various eras are clear proof that the way is open to all, even women.
c) The status of the woman in Islamic law and divine rulings
It seems what gives rise to your question regarding the status of the woman in Islam, is a series of Islamic laws that pertain to women, but with a general look at the framework of Islamic laws and the effect of gender on them, you will be able to find your answer.
Islamic laws, when looked at from a gender perspective, are divided into several categories:
1. Common rulings: such as fasting, prayer and hajj.
2. Women’s rulings: such as laws pertaining to menstruation
3. Rulings that seem to be discriminative at first sight: such as inheritance, blood money, etc.
Generally speaking, the reasons for such so called controversial rulings can be the following:
i) The man of the home is responsible for the expenditures and sustenance of the family, hence the difference of the share of inheritance compared to that of women (of course in some cases). 
ii) When some hadiths speak of women badly, what they are really speaking of aren't women in terms of them being part of the human race, but what is meant is the adoration of women. (For instance, the hadith that says: “The woman is a scorpion, but her sting is sweet”) 
iii) Some other hadiths (especially in the Nahjul-Balaghah) that scold women, are only scolding the women of Imam Ali’s (as) time who had risen against the imam in the battle of Jamal (with the leadership of Aisha). 
iv) Some rulings that aren't the responsibility of women, like initial jihad, judging, etc. aren't deprivation, but are a grace and mercy from Allah (swt) so that harsh and hard responsibilities that aren't in harmony with their delicate spirits don’t rest on their shoulders.
Imam Ali (as) says: “The woman is like a delicate and sweet-smelling flower, not like a harsh and bulky warrior.” 
v) Some rulings such as coming of age earlier than men, are so that women begin to be trained earlier so they can be ready to train future generations, especially since the age of getting married for women is lower than that of men.
vi) Some restrictions and limitations are so that some boundaries are set in order to prevent certain problems and dangers which indeed need to be prevented. For instance, women have been ordered to speak well but not in a thin and attractive voice so that “those who have sick hearts aren't tempted”. 
vii) The same way that badness and deficiency are proportional, preferring and making the man prior are also proportional. Therefore, whenever you see a limitation or reproach of women, consider it proportional. In Islam, there are numerous instances where women have been given advantages, namely:
The prophet of Islam (pbuh) said: “If you are in the middle of a mustahabb prayer and your father calls you, don’t break the prayer, but if your mother calls, break it.” 
The clear and direct command of the Quran is: “And You should treat women honourably” 
For further information, see:
Morteza Motahhari, Nezame Huquqe Zan dar Eslam
Abdullah Javadi Amoli, Zan dar Ayneye Jamal va Jalal
 "الحمد لله المتجلی لخلقه بخلقه" Nahjul-Balaghah , sermon 108.
 Abdullah Javadi Amoli, Zan dar Ayneye Jamal va Jalal, pg. 21.
 “و من آیاته ان خلق لکم من انفسکم ازواجاً لتسکنوا الیها و جعل بینکم مودة و رحمة ” Rum:21.
 “فمن تبعنی فانه منی ” Ibrahim:26.
 “من عمل صالحاً من ذکر و انثی و هو مؤمن فلنحیینه حیاة طیبة...” Nahl:97.
 “ان الذین کفروا و ما توا و هم کفار اولئک علیهم لعنة الله والملائکة والناس أجمعین” Baqarah:161.
 “وضرب الله مثلاً للذین آمنوا إمراة فرعون إذ قالت رب ابن لی عندک بیتاً فی الجنة و نجنی من فرعون و عمله و نجنی من القوم الظالمین” Tahrim:11.
 “ضرب الله مثلاً للذین کفروا امراة نوح و امراة لوط...” Tahrim:10.
 Abdullah Javadi Amoli, Zan dar Ayneye Jamal va Jalal, pg. 197.
 “خیر العلم التوحید و خیر العبادة الاستغقار” Kuleini, Usul Kafi, vol. 2, pg. 517.
 For further information on why the share of inheritance of women and their blood money is less than men’s, see: The difference of inheritance between men and women in Islamic fiqh, Question 116; The difference of blood money between men and women in Islamic fiqh, Question 117; The cases in which men and women have the same share of inheritance, Question 536 (website: 585); The equality of men and women, Question 531 (website: 579).
 Nahjul-Balaghah, short sayings, no. 61.
 For instance: Nahjul-Balaghah, sermon 80, “ان النساء النواقص الایمان...”
 “فان المراة ریحانة و لیست بقهرمانة” Nahjul-Balaghah, letter 31.
 Jame’u Ahadith al-Shia, vol. 21, pp. 428-429.
 “و عاشروهن بالمعروف” Nisa:19.