How much of a deal-breaker is having a hard time apologizing in a relationship?

That's my only flaw. I have a hard time apologizing. I tried avoiding making mistakes for that reason; so I don't find myself within an apologetic position. I hate apologizing.

I hated apologizing that as a kid, I chose getting grounded for 2 whole weeks (ego/pride) than apologizing. Well no one likes getting told to apologize. Seriously, how much of a deal-breaker is this? If you had to grade it from a 1-10 scale (10 is unbearable) how much would it be?

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To get an idea of how much I hate apologizing, this is what it would be like:
If I were ever in trouble with, got arrested and got told to apologize right now or I'll get fined and spend several days or week in jail, I'll would imagine saying ''fine, take me to jail, I'm not apologizing''.
How much of a deal-breaker is having a hard time apologizing in a relationship?
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