If the Quran states that believers are equal, whether men or women, why does only a woman need a wali to get married?
The Qur'an in several verses clearly quote the necessity of a third party which gives permission for marriage, which is the wali:
... And do not marry polytheistic men [to your women] until they believe. ...(2:221)
which is an order to the guardian of a lady not to give permission to marriage between her and a disbeliever! In my comment I've posted the wrong part of the verse, but after consulting the tafsir of imam al-Qurtobi. Note that al-Qurtobi added that in all the verses the Quran (or Allah) has addressed only males (by using the masculine form) to order or prohibit them to give permission for a marriage of the women (girls) they are in charge of! Here the tafsir part explaining the senetence translated "And do not marry"
ولا تُنْكِحُوا أي لا تزوجوا المسلمة من المشرك
(My own translation take it with the necessary care)
And do not marry means don't give in marriage a Muslim women to a pagan (man)
Note that the verb nakaha نكح here is in passive form (تُنْكِحُوا instead of the active form تَنْكِحُوا) which implies the agreement of a third person to give the permission of marriage!
And when you divorce women and they have fulfilled their term, do not prevent them from remarrying their [former] husbands if they agree among themselves on an acceptable basis. ... (2:232)
After divorce the guardian is asked here not to hinder the former spouses to remarry if they both want to get back together!
...So marry them with the permission of their people and give them their due compensation according to what is acceptable. ... (4:25)
This verse is clearly saying that a permission is needed from the guardian of the woman!
And marry the unmarried among you and the righteous among your male slaves and female slaves. ... (24:32)
Here also the owner of the slaves or their guardian is ordered to give them permission to get married.
In the Quran you may also find a clear example of a wali (a father) marrying his daughter in the story about the encounter of Musa () and the people of Median (the prophet Sho'aib):
He said, "Indeed, I wish to wed you one of these, my two daughters, on [the condition] that you serve me for eight years; but if you complete ten, it will be [as a favor] from you. And I do not wish to put you in difficulty. You will find me, if Allah wills, from among the righteous." (28:27)
so if one is a Muslim and believes that the Qur'an is the word of Allah, one has to obey and accept this that's why this fact is (and was) never questioned!
Beside those evidences you may find enough other evidences in the Prophetic traditions.
The hanafi school of fiqh however differs a bit as it allows a former married woman to decide herself without the necessity of a wali based on this sahih hadith giving the previously married woman more rights to her person.