I am a new Muslim from USA I wonder how women in Islam are equated to dogs and donkeys in the Bukhari Hadith of Sutra. If this is how Islam treats women then what all I have heard about bad treatment of women in Islam is right. I want to leave this religion.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Dear Sister,

Congratulations for having been guided by Allah to the right path of Islam, the only true religion. Allah Says (what means): {And whoever seeks a religion other than Islam, it will never be accepted of him, and in the Hereafter he will be one of the losers.} [Quran 3:85]
Know that the greatest blessing Allah bestows on the person is to guide him to Islam as Allah Says (what means): {…but Allah has conferred a favor upon you, that He has guided you to the Faith.} [Quran 49:17]

Al-Bukhari reported from ‘Aa’ishah that she said: “The things which invalidate the prayer were mentioned before me (and those were); a dog, a donkey and a woman. I said, “You have compared us (women) to donkeys and dogs. By Allah! I saw the Prophet praying while I used to lie in (my) bed between him and the Qiblah. Whenever I was in need of something, I disliked to sit and trouble the Prophet. So, I would slip away by the side of his feet.” (1.493)

Know also that Satan and his followers endeavor to prevent people from getting this Grace [i.e. of embracing Islam] In fact, Satan vowed to oppose anyone who wants to adhere to the right path as narrated in the Quran. Satan says: {… surely I will sit in wait against them (human beings) on Your Straight Path. Then I will come to them from before them and behind them, from their right and from their left, and You will not find most of them as thankful ones (i.e. they will not be dutiful to You).} [Quran 7:16-17]

So, the Muslim should beware of Satan's whispers and insinuations. You have done very well by requesting clarifications about ambiguities you find in your religion.

In fact, the Quran is full of verses about women; especially in two Soorahs (Chapters), one of which is called An-Nisaa’ (Women) [Quran 4], and it is 176 verses, and the other one which is Soorah al-Ahzaab, and it is 12 verses. These Soorahs include many rules about the woman: whether married or divorced, how to spend on her, what are her obligations, how to get her right, when it is lawful to marry her and when it is not, and so forth.

In Soorah Al Baqarah [Quran 2], there are 21 successive verses regarding women. There are also many other verses about women in Soorah An-Noor, Al Ahzaab, Al Tahreem, … etc
Many verses constitute an evidence of the high status and ranking of women in the society. Some Ansari women said during the life of the Prophet if Allah knew that there was any good in women He would have talked about them in the Quran, then Allah revealed to his Prophet (what means): {Indeed, the Muslim men and Muslim women, the believing men and believing women, the obedient men and obedient women, the truthful men and truthful women, the patient men and patient women, the humble men and humble women, the charitable men and charitable women, the fasting men and fasting women, the men who guard their private parts and the women who do so, and the men who remember Allah often and the women who do so - for them Allah has prepared forgiveness and a great reward.} [Quran 33:35]

So, there are numerous verses in the Quran about the dignity, honor and respect due to women.

Islam states that the woman is complementary with the man in building the society and keeping progeny.

Allah Says (what means): {O mankind, fear your Lord, who created you from one soul and created from it its mate and dispersed from both of them many men and women} [Quran 4:1]

The Quran informs us that the woman is equal to the man in many fields like the reward in the Hereafter and the closeness to Allah by performing good deeds. Allah Says (what means): {Never will I allow to be lost the work of any of you, be he male or female. You are (members) one of another…} [Quran 3:195]

Allah Praises men and women for performing good deeds. Allah Says (what means): {…and ask forgiveness for your sin, and also for (the sin of) believing men and believing women…} [Quran 47:19]

Indeed Islam commends men to be good to women and respect them in their role as wife, sister, daughter or mother. The Prophet in the illness that caused his death warned men not deny women their rights. Then he advised Muslims to be good to women.

Islam gave the woman an independent right of ownership free from the consent of men. She can own property and deal with it as she wishes. Allah Says (what means): {For men is a share of what the parents and close relatives leave, and for women is a share of what the parents and close relatives leave, be it little or much - an obligatory share.} [Quran 4:7]

What we have cited is clear evidence that in Islam women are not compared with animals.
As for the Hadeeth you mentioned, we say the following:

First, there is no Hadeeth that compares women to dogs or donkeys.

Actually, the Hadeeth refers to three things that the prayer i.e. reduce its reward. But this does not mean that women and animals are similar. Actually ‘Aa’ishah The Mother of Believers was the first to deny the authenticity of this Hadeeth saying: “They (those who narrated this Hadeeth) compared us with donkeys and dogs. By Allah, I saw the Prophet praying and I was lying in bed between him and the Qiblah (i.e. in front of him)”. [Al-Bukhari]

This is an evidence that the Prophet used to pray while a woman was in front of him. Some believe the reason he did so was that she was his wife and he had no fear of being tempted by her. Others say that it was during the night prayer and the room was dark. Others believe that praying this way was particular to the Prophet who could control himself more than anybody else.

No matter what the reason, for sure the Prophet prayed while ‘Aa’ishah was in front of him.

There is disagreement among the scholars on whether the Hadeeth you mentioned is in effect. Most of them believe that this Hadeeth is abrogated by ‘Aa’ishah’s Hadeeth. This opinion is correct.

Allah knows best.