could someone, please, tell me why my wisteria never flowers.

It is possible you have a poor clone(sort).

What can I do about that? Shall I prune it right back and see what happens next year?

Oh lord, no, don't do that. Wisteria is notoriously difficult - it needs pruning correctly twice a year, and a good amount of sun to flower at all. Being left to grow as it wants, you'll never get a flower, and they don't often flower much before 5-7 years old anyway. Check out how to prune it properly (its quite complicated) and have patience. Should have been pruned in August and then needs it again in February, so I think you should make a start now! This is how it should have been done:
You need preferably to restrict the number of mainstems - if you only want one, let it get to the height you want, then cut off the top, if you want 2 or 3, the same applies. Then you should start getting shoots that grow sideways (laterals). In august, these need reducing by half. In February,prune the laterals back again, this time to 2 buds. Keep an eye on the main stem/s and "rub out" any budding growth, or remove with secateurs. Good luck..