First check whether the setup is complete, i.e. bait, lure, bobber, etc. The slot number of the rod should be green. If it's red you are missing something. If all slots are green, then it probably is a bug.
I have encountered this bug several times, and while annoying, can usually be solved by restarting the game. Don't leave the lake. Just restart and see if that fixes it. Sometimes you can work around this by going to the inventory, cycle to the rod you want, then back to the lake. Im on ps4, so it would be Options, rod 3, options again.
All else fails, email support. You'll get a quicker response than in here.