No way he can win with 〜っこない

Grammar Explanation: A strong denial with 〜っこない

As he performs one trick after another, Kaito says he’s unbeatable at magic. Aoko says he can’t win against Kaitou Kid, the magic-using thief her police father has yet to apprehend. Kaito disregards the claim and continues disrupting class with his tricks.

青子(あおこ):: 「なによ、かっこつけちゃって…　勝(か)てっこないじゃない……」; “What's with all that showing off? There's no way he can win.”; Literal: “What is that, acting cool... There is no way he can win, is there...”; 「お父(とう)さんだって、手(て)を焼(や)いてるんだから」; “Even Dad is having a hard time of it.”

Key Points

1〜っこない is emphatic impossibility

勝(か)てっこない says winning is not merely unlikely; Aoko treats it as impossible.
It attaches to the verb stem: 勝(か)てる becomes 勝(か)てっこない.

2The target is understood from context

The line does not repeat Kaitou Kid, but the previous exchange makes him the person Kaito supposedly cannot beat.
じゃない turns the claim into a pointed assertion.

3だって supports the judgment with evidence

お父(とう)さんだって means “even Dad”, strengthening the argument because her police father struggles too.
Aoko is not just insulting Kaito’s confidence; she backs it up by pointing to someone more experienced.

4手(て)を焼(や)く = to be at one’s wits’ end with something

手(て)を焼(や)いてる is the progressive form, so her father is currently having a hard time dealing with Kaitou Kid.
The idiom often implies that the problem is troublesome to handle, not just briefly difficult.

さん is an honorific suffix attached to a person’s name to show respect and social distance, roughly equivalent to “Mr.”, “Ms.”, or “Mrs.” in English, though it’s used far more broadly and doesn’t specify gender or marital status.