responses to evolution explanations

You don't have proof.
        (Science doesn't deal in absolute proofs in almost all cases. It deals with a preponderance of evidence, and/or with agreeing evidence from different approaches.)

Our explanation is as good as your explanation.
   (This is the different worldviews approach. We have the same data (accumulated, of course, by scientists who in the vast majority of cases are not YECs or ID proponents)  and we view it through the lenses of our different worldviews.
   So the two conclusions can be considered to be equally valid (?) even though they conflict. Two explanations for the same evidence.
related to this is the ides that evolution a sa  different worldview also can be counted as a religion, a belief, a result of faith. If creation doesn't belong in science classrooms because it is a religious belief, then neither does evolution.

Here is something I don't know. From this argument - same data, different interpretation, what would the response be to the situation that the evolution argument is valid for its worldview basedon the jointly accepted evidence?)

Our explanation fits the evidence better than the evolution explanation

Your claim is impossible.
      (examples -
no one has seen life come from non-life.
some mathematical formula that is supposed to show that evolution of proteins is impossible. Information only comes form intelligent sources.
There can be no new information added to the genome just by mutations.)

Other approaches include:
 the appeal to common sense.

"Were you there?" since we cannot directly observe the past, we can't know what happened. Science assumes that things haven't changed - not always clear what specifically they mean) so that assumptions from measurements of the present cannot be safely applied to the past. for instance, physical constants: did the speed of light remain constant? radioactive rates of decay? In addition I think there is a confusion in use of catastrophism and uniformitarianism.