The reason it is considered makrooh by the South Asian Scholars is because they believe it is considered "dis-respectful" clothing.
But that just fall under the matter of opinion, A t-shirt still covers a mans satar. The hanafi scholars in the middle east have no problem with half sleeves.
There are two issues here:
1. Leaving the elbows/arms uncovered
2. Wearing clothing that one would not go out with in public.
As for the first, I have yet to come across a statement in any of the Hanafi books of fiqh, stating this to be Makruh. I have searched in detail, have asked numerous Muftis, but no one has been able to produce one such ruling from the reliable books of the madhab.
The Fiqh books mention the issue of folding sleeves, however this is makruh due to it being forbidden in Hadith, as one would be preventing the sleeves from making sajdah.
Some Urdu Fatawa use the texts on folding the sleeves for t-shirts, however those texts don't apply here.
As for the second, maybe 50 years ago, wearing a short-sleeve shirt or a T-shirt would have been something one would not wear out in public.
Today, people wear it everywhere, so it isn't classfied as thiyab al-bidhlah ie. clothing one wouldn't wear in public. It is makruh to perform salah in things like pyjama's, as these wouldn't be worn in public. Short-sleeves are not so.
So one is allowed to perform salah in clothing that is short-sleeved, as long as it is such clothing that one would normally wear in public.
As for Nabi's qamis sleeves being until the wrists, that doesn't necessitate shorter sleeves being makruh, just as it doesn't negate other items of Nabi having shorter sleeves. In fact, some of the clothing attributed to Nabi in museums do have short sleeves, even though this isn't proof.
It is for this reason, that the normally very strict author of Ahsan al-Fatawa, Mufti Rashid Ahmed Ludhyanwi, clearly gave permission for salah with a short sleeve kurta.
Se Ahsan al-Fatawa Vol. 3 Pg. 407-408.
And Allah Ta'ala knows best
Sahabah رضي الله عنهم would cling fast to the Sunnah, on account of it being Sunnah, while we discard the Sunnah, on account of it being (just) Sunnah!
Great answer as usual.
I've lead prayers quite a few times with those short sleeved Arabian thawbs/jubbas. I get some weird looks from TJ's and Sufis and hardcore Hanafis, but since the general typical American Muslim couldn't care less, I go with the oppressed majority.
Also at the time of the Prophet, they barely had enough clothes to cover their Satar and body!
What i was saying, is that it is makruh to pray in a kurta, which was actually full-sleeve, but the sleeves were folded to make it a half-sleeve one. I have read hadeeth on its prohibition.
There are narrations in Quduri, where it is mentioned that the people offered their prayers when they were totally naked, because they had nothing to cover themselves.
So, a mufti can not issue a fatwa, that it is ok to pray when you are naked.
I have read in all the hanafi manuals, in my madressah and darul-ifta, that praying in short-sleeves is makruh, and the sunnah is to pray in full-sleeves.
Therefore, the rulings have to be deduced from sunnah "amaals", and not mere incidents. And our success lies in following the sunnah of Rasoolulah (SAWW).