There's a pretty good explanation of the reality and need for Purgatory in this link.
Catholic Bible 101
If there is no Purgatory, then we have the absurd situation of a serial murderer (or an Adolf Hitler to take a more extreme example) who makes a sincere deathbed confession, and then waltzes straight into heaven, without in his life ever having made any attempt at personal santification.
HItler's rages, his blaming of other people, his cruelty, his vindictiveness - all is suddenly sweetness and light, without his ever having made one ounce of effort to reform his character, other than a last minute realisation of what a mongrel he'd really been.
No problem - just come straight in!
NOBODY gets into heaven unless they are
literally perfect, and this means purfication after death if necessary. Christ's death on the cross means we are not condemned - it doesn't mean we are automatically made pure. I don't know about you, but I think I sin every day, usually in a venial way, but sometimes more seriously.
The man who wasn't even properly dressed for the heavenly wedding got thrown out on his ear. I believe that parable at least contained an inbuilt reference to Purgatory.