The life of a professor, as their career progresses is never getting easier, at least if they are serious about their research. There is a neverending stream of academic chores (grant writing, teaching, faculty meetings, conferences) and in between there is a little time left for research. But progress in research is critical since everything else depends on it.
Needless to say, there is sometimes a bit of frustration, and professors, in their relationships with people, may appear brusque or rude. When you have 45 seconds to respond to a mail, you may write something like:
It's in the chat.
as an answer to a carefully worded and polite question about some missing assignment or syllabus, or whatever one of the students didn't understand. If you have a minute and 45 seconds, you might think that this is your third student who wrote you about this, when everyone else didn't need additional clarification. Given the additional time, you may write more, and you might be rude. Especially rude if your wife is calling you for the third time to remind you her friends are coming to dinner, so you better not be late.
Actually, you may come across as rude when answering to your own friends, whom you actually like. They call you to congratulate you on your birthday, and you cut them short saying you're running late to a class where students are not getting the syllabus, or whatever, because you're too overwhelmed with other things. Again, the other things, may be a million and they all need your time.
There are research-first professors and there are professors who put teaching in the first place. The first usually get to teach the graduate students, exactly because they tend to skimp on niceties. The second (at least in US universities) get to teach undergraduates, and they are usually nicer, and teach better.
Unfortunately, when you chose an academic adviser, you choose from the first category. Some are rude, some are just exasperated that deadlines are approaching and their postdocs/students aren't making progress. What I'm trying to say is that your perception of their email should not be the basis for your choice of an adviser.
Some others advised to check their publication record, talk to their students, and see where the group alumni continued their careers. If the atmosphere in the group is not good (too competitive environment, abusive behavior, etc.) that's a much more serious red flag than a seemingly rude email. As a general rule, look at what that guy is doing, rather than judge what they say. Think about this. Your post makes you appear entitled. But, I don't know you, and it's very possible you've only dealt with very nice teachers up to this point. "Nice" is what I was when I was teaching introductory classes. "Nice" doubles your workload, without necessarily providing significant extra value to your students.