I will use the explanation in this site as an example of what looks to me as a wrong explanation of why acceleration in uniform circular motion is centripetal.
This site, as other sources, reasons as follows:
- it vectorially obtains the difference v final minus v original;
- notes that the resultant arrow more or less points towards the centre of the circle, like here:
- and concludes: you see, we have proved that the acceleration is centripetal.
I have no doubt that the instantaneous acceleration is centripetal, but here they are showing the average acceleration and I am not sure that the latter is also centripetal.
A clue: make the interval 180 degrees and the same exercise shows that the length of the change of velocity vector is doubling the v initial vector and it is pointing, logically, in the opposite direction; make it 360 degrees and, logically, the change of velocity vector is 0 and pointing nowhere…
I suspect that, even in the original example of the site, the operation, if well done, should not show that the change of velocity vector is pointing towards the center, but in a direction justifying precisely how much the particle has changed its direction from point A to B and that, if their drawing shows a center-seeking arrow, it is only because it has been (unconsciously) re-arranged to that end.
Would you agree to this or did I miss anything?