Why do tigers have sharp teeth? To rip flesh.

No.

Why do tigers have sharp teeth? Because their ancestors who had sharper teeth produced more offspring than their relatives who did not.

In Aristotle's language, ripping teeth may be a cause, but it's not the Final cause, and that's what we're talking about.

The reason biologists don't like the teleological explanation is that (a) it tends to make people think of a creator, as you say, but also (b) it describes traits as "solutions" to specific "problems" (e.g. the problem of ripping flesh), but the issue is that, starting from the pre-sharp-toothed ancestor, there were infinitely many possible directions evolution could have taken that would never have needed to solve this "problem." The existence of the problem (cutting meat) and the random path that led to the tigers being carnivorous are actually one-and-the-same. If you didn't have sharp teeth, you wouldn't have needed them.