Also, I can't say I perceive the dismissal from the quote alone. Those two short sentences feel like a very brief excerpt from beginning of a conversation so it's hard to gauge, but I feel that it's an exclamation of surprise that's non-committal and lacking an explicit offer to proceed with details, rather than dismissive (or worse). Circumstances, tone, body language, relationship and other things may make it vary, of course. Can't say it's arrogant either, "no way, it must work" is a legit exclamation that doesn't imply incompetence (unless, again, tone etc).
I'd say it's just passive, not taking any initiative to troubleshoot and communicating just the assurance that the problem must be solvable, then bouncing back to the inquirer. In my understanding, it's more of a lazy/not being in the mood, not dismissive (and I'd have a really hard time trying to call it "toxic").