Has there ever been a period in history when evolution occurred faster than extinction?
Do you have proof of such a period occurring, or do you simply assume that it must have occurred because otherwise evolution can't be true?
Why would single celled organisms, over time, evolve into things such as whales or dinosaurs when single cells are more fit to survive, and can in fact easily mutate to remain survivable?
I'm just asking questions here as a layman! :-)
You mean, recorded history?
You're neglecting a great deal of anthropogenic bias here. First of all, we're spending much more time looking for extinction rather than looking for speciation; and we're hyping the former. And second, we really are changing the world rapidly, and therefore may well be killing species off faster than we're causing new species to evolve. The question needs to be answered over the long term.
If I wanted to argue dishonestly here, I'd claim that, for example, there are more species of wild birds in the continental US now than there were in 1904. In that time we've lost three undisputed species - the passenger pigeon, ivory-billed woodpecker, and Bachman's warbler - but we've gained at least 8 new species of crossbill. Now, it is likely all that happened with the crossbills is that we noticed that superficially similar crossbills are actually divided into 9 different groups that don't interbreed, but the fact is that much speciation is a gradual process, and it's arbitrary where we draw the line. So were there 9 species of common crossbill in 1900? I don't know, and no-one else does either.