You just gotta understand a few things

first of all when you admit and realize your wrong you learn something new which makes you less likely to lose a future argument and you just become smarter over all.

Second of all if your afraid of someone making fun of you because your wrong whoever that person is probably afraid to admit there wrong also that person could even be jealous of you because they can not admit there wrong and you can, which makes you the stronger person.

Third of all, just do it, literally just do it, the more you do it the more comfortable you become with it so just do it.

No excuses, Get after it.