It's hypothetically possible that bad things happen to good people. But it's pretty rare because in most cases you had to make some bad choices to even get into the position where something like that could happen.

1. Industry culture is not very tolerant of serious criminal history, the notable exception is probably DUI. Anything showing lack of character or ethics is a huge red flag, DUI or domestic violence may be heat of the moment but anything involving theft or dishonesty will be a problem. It helps if you were young, they know people mature with age but it sounds like that's not the case.

2. They are concerned with two issues:
a) Have you reformed, learned your lesson, etc. You convince them by taking FULL responsibility, tell them what you learned, that your regret your behavior, and how you're now a better person.
b) They are also concerned with how your record will reflect on the company if you get in the news media due to accident or incident. You can do nothing to *convince* them on this issue, they'll make their own decision.

3. An ATP requires that you be "of good moral character". This is nebulously defined and inconsistently enforced but a significant non-DUI felony might prevent you from holding an ATP pilot certificate.

4. You also need a 1st class medical, and they will sometimes deny those based on criminal history due to concerns about mental health (anti-social personality disorder).

5. "Bad Things Happen to Good People" is not an attitude that accepts responsibility. Most of us in and around aviation make some significant efforts to ensure that this sort of bad thing does NOT happen to us. I can 100% guarantee that you will be declined if you express a "poop happens" attitude at an interview.