So basically, for Popper's falsificationism to work, there needs to be an objective way by which we can compare two competing theories' "empirical contents", ie their actual (explanatory) predictions and what would make one or the other falsified. And for the most part, in ordinary science, there is. Competing theories generally operate within a single "paradigm", and often differ only by tiny details. Successive theories make very small changes to their predecessors, and this is how Popper thought we approximated something like truth ("verisimilitude").
Except sometimes, this isn't the case. Sometimes, there are enormous revolutions in scientific understanding which go beyond a Popperian framework of falsification. Kuhn called these periods of non-ordinary or revolutionary science "paradigm shifts", and yes, it's Kuhn you have to blame for every TEDx asshole who has since used or misused the phrase (tbh Kuhn himself is among these). We can think of lots: Aristotlean to Newtonian physics, for example; or Newtownian to Einsteinian. But let's see where thing actually break down.
The first fracture is the fact that theories from different paradigms may actually be non-comparable, or "incommensurable", when they employ entirely different taxonomies. Imagine I brought back a medieval Aristotlean and asked you to prove his worldview wrong—do you think it'd be easy, if at all possible? Some think we can create "shared taxonomies", ie shared spaces of overlap between paradigms where discussion and comparison is possible. But there's no reason this has to be the case, and even if it is, it's at least plausible that two paradigms could be entirely incommensurable in how they describe the world.
Second and more fundamentally, observations are always and unavoidably ""value-laden"". What makes you think you ""observed"" a passing planetary body is actually a bundle of theories, including the theory that you can rely on your own eyesight and the instruments you use to view the body (telescopes). Sometimes called the Quine-Duhem thesis, this is pretty much fatal to Popperian falsificationism.
The famous example is those observed anomalies in the procession/perehelion of Mercury, which were known, as early as 1915, to present a substantial ""falsification""" of Einsteinian relativity. Except… what happened? Did everybody go on and give up on Einsteinian physics, like good Popperians? No, you idiot, they accepted the observations as "anomalies"; things which couldn't be accounted for by the theory, and which presented avenues for further inquiry; until the 1970s when it was realized it was something to do with how we measured the things in the first place.
Let this suffice as a brief overview of why virtually nobody in this day and age subscribes to Popperian falsificationism. Lakatos, Popper's disciple, (and ironically a Marxist) would go on to refine the falsificationist framework by making it sensitive to different "research programmes", but he still had to end up, like Popper, assuming some universal set of scientific values by which we could judge the success of competing but (supposedly) "incommensurable" programmes (ie paradigms).
I should note, that while were few people today would say that any such set of universal values does exist, the Kuhnian "historical turn" should not be confused with scientific relativism, in the way in which it's understood in the popular imagination. That's closer to the attack on scientific rationality which came from sociology, (David Bloor specifically) in the 80s/90s, in a movement which is generally termed the "Sociology of Scientific Knowledge", or SSK. Both Kuhn and Feyarabend, believed in some (haphazard or wayward or miraculous) mechanism of scientific progress, and Kuhn at least was on better days "horrified" but the relaitivism he seemed to have unwittingly unleashed in phil of science. Yet we can't go back, (at least those of us who've actually been following), and if we want to criticize EVO as "unfalsifiable" it will have to be in light of these developments.
I'm going to type out something further on the actual "evolutionary theory is a tautology" argument, which believe it or not is accepted as a legitimate problem for philosophy of biology. Then I'm going to explain why this doesn't work to support your wack-ass inference to intelligent design, despite and in light of some (smart) contemporary defenders. Hopefully the thread's still up, gotta shit.