Apologizing first isn’t losing the fight. It’s just getting back to the table before everyone else.

Whoever apologizes first tends to be treated as having lost, which is why two people can sit there for days waiting. The wait is not a contest though, it is just both of you staying uncomfortable to protect a position. Going first is not a confession that all of it was your fault. It is a decision that the argument has taken up enough of the week.

Own your specific part and nothing beyond it, then say you would rather be fine with them. Most people meet you there faster than you expect. If somebody uses it against you, you learned something that was going to matter eventually.