From Longman Dictionary of Contemporary Englishthen/there againthen/there againspoken used to introduce an idea or fact that is different from something you have just said, or makes it seem less likely to be trueShe says she’s thirty-five. But then again she might be lying. →again
Examples from the Corpus
But then again• In the poll I mean. But then again..• Her world will be that good. But then again, it might not.• Children. But then again our world is suddenly very full, humanly, full of faces and voices.• Nguyen Seth hadn't changed since then, Duroc knew. But then again, the Elder was older than he looked.• If so, there was danger all round ... That niceyounggirl. But then again, was she nice?• Now, I haven't exactly got a lot of experience in this area. But then again, who has?