They argue that as here woman, dogs & donkeys are mentioned together so this is a degradation of women.

The notion is refuted in the very same tradition:

Infact if one is in his senses than the very text of the Hadith shows that its not Islam that-God Forbid!!- considers women as donkeys or dogs but it was the understanding of certain people whom Sayyidah Aisha (RA) rebuked. Again read the translation of the Hadith with special attention to the words emphasized.

Narrated 'Aisha: The things which annul prayers 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 Qibla. 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."(Bukhari , Hadith 484)

It’s plain enough that some people mentioned the things which, according to their understanding, annulled prayers and they mentioned "dog, donkey & woman".But then Sayyidah Aisha (RA) rebuked them by saying "You have compared us (women) to donkeys and dogs" and then she clarifies that this not something taught by the Messenger of ALLAH (pbuh) as, she said; "By Allah! I saw the Prophet praying while I used to lie in (my) bed between him and the Qibla."So where is the confusion? The problem is the same that I often mention that these missionaries, these devil incarnates yell such obscenities only in an attempt to get rid of their frustration that they have when they see Islam as the fastest growing religion of the world.

Other Hadith and meaning of the ‘annulment of Salah’:

Now some people may bring some more Ahadith from the Holy Prophet (PBUH) himself like the following;

Narrated Abdullah ibn Abbas: Ikrimah reported on the authority of Ibn Abbas, saying: I think the Messenger of Allah (peace be upon him) said: "When one of you prays without a sutrah, a dog, an ass, a pig, a Jew, a Magian, and a woman cut off his prayer, but it will suffice if they pass in front of him at a distance of over a stone's throw." (Abu Dawud, Hadith 703. Albani classified it as Da’if)

Abu Huraira reported: The Messenger of Allah (May peace be upon him) said: "A woman, an ass and a dog disrupt the prayer, but something like the back of a saddle guards against that." (Muslim, Hadith 790)

But even these Ahadith never mean that these things annul the prayers, it only means that they can divert ones attention, they disrupt the prayers.

Imam Nawawi, a famous Scholar writes in his commentary to this hadith from Sahih Muslim;

"Here disruption only means to have a negative effect on the prayers by the way of occupation of heart in these things." (Sharah Al-Nawawi 2/266).

All these things mentioned here can disrupt one's attention. A Jew because of his particular appearance and the fact that they were having a row with Muslims then, seeing an adversary can obviously distract one's attention. A pig or an ass can become a source of distraction because of their course and loud voice and bad smell, a Magian because of his unusual appearance (see from the point of view of Arabs then). And a woman could distract because of her beauty while prayers need full time attention.This is enough to prove that it’s only about being a cause of distraction that women are mentioned with all these things. It’s not that-God Forbid!-some parallel is drawn here.

Its not to degrade woman. Read the following!

Now its not degradation for the females but only the truth is mentioned that if a woman passes in front of a man, this can get his attention diverted and that will effect the quality & sincerity of ones prayers. It never means that, God-Forbid, a parallel is being drawn between woman and other things mentioned. These are mentioned together only because they can divert ones attention.See its just as if a person says; "Humans, dogs & donkeys are all living beings", this does not mean that humans are considered equal or same as dogs & donkeys or some parallel is being drawn between all these. Or does it?

It’s about mature women only:

And this is said for the grown up women only not small kids for they cannot divert ones attention in that sense.

Narrated Abdullah ibn Abbas: Qatadah said: I heard Jabir ibn Zayd who reported on the authority of Ibn Abbas; and Shu'bah reported the Prophet (peace be upon him) as saying: "A menstruating (i.e. grown up) woman and a dog cut off the prayer." (Abu Dawud, Hadith 704. Albani classified it as Sahih)

Nothing annuls Salah as such:

Nothing annuls the Salah as such but these things can disrupt ones attention. Read the following Hadith;

Narrated Ayyash bin Abu Rabiya:The Prophet (pbuh) said: “Nothing annuls prayers.” (Sunan Darqutni, Hadith 1396. Ibn Hujr classified ir as Hasan in al-Diraya 1/178)

In the end I'll only repeat a statement of Sayyidah Aisha (RA) from the very Hadith the heathen bring forward; "By Allah! I saw the Prophet praying while I used to lie in (my) bed between him and the Qibla."

Hope all this will help understand!

INDEED ALLAH KNOWS THE BEST!