I definitely would not say that his putting off meeting your four kids is a bad sign or a red flag, but I do think a discussion about the issue is not only warranted but probably long overdue. When he says “it’s bad timing,” you need to ask him what he means by that. Meeting a significant other’s children is a really big deal. At least, it should be. I’m of the mind that that kind of introduction should be reserved for relationships that are monogamous and on the track to commitment. As a mother, you should be of that mind as well. And, if this guy has any sense, he should feel the same way. And maybe he just doesn’t feel that your relationship is at the level yet that he should be getting involved with your children. Maybe he can’t say with confidence that he sees himself in your lives months from now, and so he doesn’t want to get attached to your kids (and vice versa) if he isn’t there yet. That doesn’t mean he won’t get there. It may just mean that he needs a little more time. Conversely, the idea of four children may scare the shit out of him and he might prefer to pretend that they don’t really exist (which is hard to do once you’ve met them).
Whatever his reasoning is, you obviously need and deserve to know what it is. Is this relationship maybe leading somewhere serious or not? If he can’t give you an answer, then you need to decide whether you’re willing to give this relationship more time — without pressuring him to meet your children and move faster than he’s ready. If it turns out you’re on different pages and you don’t feel like waiting for him to catch up, you might want to MOA.
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