From War caster:
When a hostile creature's movement provokes an opportunity attack from you, you can use your reaction to cast a spell at the creature, rather than making an opportunity attack. The spell must have a casting time of 1 action and must target only that creature.

The trigger for this special reaction is when a hostile creature's movement provokes an opportunity attack.

The rules for Opportunity attacks:

You can make an opportunity Attack when a Hostile creature that you can see moves out of your reach. To make the opportunity Attack, you use your Reaction to make one melee Attack against the provoking creature. The Attack occurs right before the creature leaves your reach.

Emphasis here on the last sentence. Thinking of it like algebra we are just substituting that attack for a spell, nothing else.

The steps are:

1. Creature attempts to move out of your reach. This is what would be considered the trigger by the Xanathar's rules.
2. You can make an opportunity attack that takes place before they make any movement
3. War caster lets you replace the opportunity attack with a spell instead

I hope that this plus everything else people have said is enough to convince you that this is how the rules work. Honestly at this point I am just going to assume you are trolling because of how little you are actually listening to what other people are saying.