It is a phrase that means "to talk at cross-purposes". It is used when describing a situation in which people are not on the same wavelength. You feel that the person who you talk to misses the point of the topic.
ケンとはもう連絡を取っていない。彼はいい人だけど、話が噛み合わない気がする。
- Meg: You don't look well. Is everything okay?
元気ないね。大丈夫? - Amy: Um, I got into a little fight with Jim. We ended up quarreling because we talked past each other. Hmm, I feel that I can't get through to him sometimes.
んー、ジムと喧嘩しちゃった。話が噛み合わなくて、遣り合っちゃった(or喧嘩しちゃった)。んー、時々話が通じない気がする。 - Meg: I see. Do you think it comes from linguistic and cultural differences?
そうなんだ。言語や文化の違いだと思う? - Amy: Hmm, I don't want to think like that and it is not only that. Not being on the same wavelength with your significant other is painful.
んー、そういう風に考えたくないし、それだけじゃないと思う。好きな人と話が噛み合わないのは、辛いな。