Can I become a professor if I were expelled from the uni? I’d just like to know your opinion on this issue (whether you think it is ethical or not).
The point is, for three years, I was a straight A-student. But towards the final year, I simply started to burn out, but then I didn’t know how to handle the situation and my mental and physical health deteriorated.
As a result, I got an F. At our university, if you get an unsatisfactory mark (F) you have to take summer classes. Even though it was the final year, students were still allowed to take them.
I didn’t consider taking a leave of absence since the reason is not considered serious enough in my country.
Then I thought about taking a year off by withdrawing. But I was recommended to stay since a few years of my studies were financed.
This year, the rules were changed and now, as it is the final year, those who got unsatisfactory marks are expelled. So was I.
In my country, however, one is allowed to be enrolled in the college again, retake some classes and get a diploma. And this doesn’t prevent you from getting into grad school.
So the question is, do I still have a moral right to become a professor at another university?
I think that if I’m going to pursue Master’s degree in another university and (on condition that my performance is great) this university is interested in having me as an academic, I should be transparent about this fact.
Or do you think that it is better for me not to pursue academic career at all?
Would a student like that have a chance in your country?
Update: I was eventually given the opportunity to withdraw (since the documents are yet to be signed) and enrol in the same university next year.
Thank you everyone for your answers!
Yes, you can become a professor. Your expulsion (for unsatisfactory marks) seems equivalent to failing your degree. Failing a degree doesn't preclude becoming professor. But you'll (likely) need a degree to become one. (The definition of professor varies between countries.)
From comments:

[is] failing a degree...dishonourable...something [to] be ashamed of?

Failure isn't shameful nor disgraceful: A professor who hasn't failed, hasn't challenged themselves enough.

Do you think, as a professor, you have the right to keep it to yourself or be transparent?

In the immediate future, universities and employers will want to know why you dropped out, failed, were excluded, however you want to phrase it. Just be honest. Explain your situation. You were burning out, deteriorating mentally and physically, these aren't shameful/disgraceful events.
A professor (depending on definition) probably need never mention distant failures: In the future, historic details (even failing a degree) become irrelevant.