You've only been dating him for 5 months. I think that's too early to have your children meet him. Like some other moms have said, his kids are adults. They are more capable of understanding "dating" and that sometimes "dating" someone doesn't lead to a permanent relationship. They will be far less affected by dad "seeing" a nice woman that they like if things don't work out.
Younger kids have a harder time with that. I've seen it with kids of some friends of mine. They are of the opinion that it's them AND their kids or it's nothing. That's fine to an extent, but I don't think kids need to meet every man that you go out to dinner with maybe once or twice then there's a different one next week. It takes time to figure out if you even like seeing a movie with a person, let alone want to persue a serious relationship with them. I personally don't think kids need to be involved in all those ups and downs.
I'm not saying you've done that at all, but 5 months is early, in my opinion, and it seems to me the man you're seeing is very aware of what can happen when kids and adults get attached but things don't work out. I wouldn't assume that he doesn't care about you or doesn't think that you have really nice children. I would assume the opposite. Maybe he cares enough not to want to rush things where your kids are involved.
I don't think backing out of a planned outing was nice at all, especially if he didn't come right out and tell you it's because he was afraid or thinks it's too early.
I would relax for now about him meeting your kids. You say your kids really want to meet him so they are aware you are seeing him. Maybe he's worried about their perception of what his place in your life is, etc.
If you're both talking marriage and he's afraid to meet your kids, that's obviously a problem. But, if you are just at the "dating" stage, I would have an honest conversation with him about how he's feeling regarding meeting your kids. If he thinks it's just too early, that's not a bad answer.
That's just my opinion.
Of course, everything isn't all up to him and if you feel that after 5 months a man should be getting involved in your kids lives and won't, then you can end the relationship and be glad that your kids weren't involved, no harm done.
I've been single for 14 years. By choice. But, I've dated. My dids didn't even know. I've gone out to dinner and dancing when my kids were with their dad or spending the night with friends. I didn't tell my kids "I went here and there and we did this and that"....of course kids are going to want to go too. But I can't tell you how many times I knew after one meal with someone, that I had no interest in seeing them again. There was no reason for my kids to even know I went to dinner.
I've had one serious relationship since my divorce. And it was serious. I met him through mutual friends and I was so protective of myself and my kids, I didn't even give the guy my phone number for 3 months. I called him. We talked and went out, I really liked him. One day when he was at work, I called and left a message. The only thing I said was my phone number. We saw each other for a year before I introduced the kids and they fell completely in love with him. We wanted to get married. His parents were elderly and his mother fell ill so he moved away to take care of them. Emotionally, it hurt worse than my divorce because we loved each other and we got along so well. It devastated my kids. I couldn't blame him for racing home and doing right by his folks, but it ripped our hearts out. He never did marry anyone else and neither have I. The last time I talked to him he said leaving us was the biggest mistake he ever made in his life.
We got word he passed away unexpectedly last November.
I'm not sorry my kids had the time they did with him because he was so amazing and showed them so much love. But, I wish I could have spared them how much it hurt when it was over. And it did hurt.
Anyway, like I said, I would relax a bit about it for now.
He may be worrying that once he meets your kids, that means that committment is required and maybe after only 5 months, he's not sure what the perameters of that "committment" means.
I wish you the best, I really do.
Sometimes the best things are the ones you slow down and take your time waiting for.