What would be your reasons for avoiding to talk about your girlfriend?

I started to be attracted to a new coworker I thought he was single for a few weeks then he briefly mentioned his girlfriend in a meeting so that was disappointing. He flew out to meet us in person (remote position). He never talked about her and I tried to inquire but he gave one word almost annoyed sounding answers. He also spent his vacation meeting us and talks about getting a visa to move. It sounds to me like he’s not that invested in his girlfriend. I don’t plan on crossing any boundaries I just wonder if they might be on the outs?
What would be your reasons for avoiding to talk about your girlfriend?
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