I just replace the clutch cable for my motorcycle Honda VTX 1300 and now it won't start?

I was told that it has to do with some loose cables by the clutch, but it all seems to be fine

I doubt it's clutch cable related. The cable just operated the clutch mechanism.

There could be however a safety switch that tells the bike whether you're in neutral or not, which you could have loosened or something. Usually, a bike with a neutral safety switch, won't allow the bike to start in gear if the clutch lever is not held in. This is obviously to stop the bike jumping forwards and potentially causing an accident.

So… Make sure you're starting the bike in neutral.
Make sure the neutral light is working.

If it isn't, you can bypass it via holding in the clutch lever. Make sure you're in neutral first though, as if you accidently start it in gear and loose the clutch lever out without realising, you could have problems.

The two wires that go to the safety switch are off.

I can't tell you the reason why it won't start but I can say that's clutch cable shouldn't be the reason unless there are some safety wires that are loose. Is it turning over or not?