'A win' means that you won. 'A defeat' means that you were defeated. It means that someone defeated you. These are clearly opposites. I think that your confusion comes from thinking of the verbs 'win' and 'defeat' as synonyms. They aren't synonyms. They are used in different ways. One refers to the winner, one to the loser. You can say 'United won the match' or simply 'United won'. You can also say 'United had a win'. What you can't say is *'United defeated the match' or *'United defeated'. This makes no sense. If you use the word 'defeat' you have to say WHO was defeated. For example 'United defeated City' or 'City was defeated by United' or simply 'City was defeated'. And if you want to use a noun to say what happened to City, you'd say that they experienced a defeat.

The main difference in their usage as a verb is that you generally win a game or contest, while you defeat another person or team. If I compete against someone in chess and I win, I can say "I defeated him", but not "I won him". I can say "I won the chess game", but not "I defeated the chess game". The only way the second option might be possible is if you're playing against a computer, so the game and your opponent are the same thing.