My experience is that the float bowl will get a dab of water-- from rain, washing or the tank-- and this can wick up into the jet threads, and if the bike is left sitting for a long time the water will corrode (oxidize) the carb pot metal (a zinc-aluminum alloy) and lock the jet in. As Wirespokes says, penetrating oil, heat cycling and when the jet starts to move, turn it back and forth as the corrosion bond breaks down.
Tricky, but do-able if you're careful. Brute force usually results in a cha-ching sound emanating from the wallet.
'73 R60/5 Toaster