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Are you sure that it involves fighting? With airplanes the term is used for landing in heavy crosswinds by pointing the plane to the side and landing sort of sideways (the way crabs walk). It sounds like it could be related.
Explanation: It is hard to be sure without any context, but I believe that 'to crab' is really not a special term in falconry at all and just has the same general meaning it has in other contexts of a 'sideways' crab-like movement. Since the normal German translation for this sort of movement ("sich im Krebsgang bewegen") is a really bad fit for aerial manouvers, I would suggest that you paraphrase it with an expression that captures the sideways character of the movement but leaves crabs out of it.
Lars Helbig Germany Local time: 09:37 Native speaker of: German