To be fair, the problem US Shermans had with German tanks was partly doctrinal. US Army doctrine was to fight enemy tanks with “tank destroyers,” an up-gunned tank-like vehicle used mostly from ambush, not tanks – true tanks were for advancing through enemy defenses (which, by definition, were not tank-heavy, since the Germans concentrated their tanks into offensive striking columns). So the Shermans were not really expected to fight tanks…according to the high-level planners.
It’s sort of analogous to the situation with battlecruisers, which had been designed for a particular use (hunting weaker ships) but looked like battleships, so they were put into the line of battle against battleships. Tanks looked like the right thing to fight other tanks – the first thing any infantry commander would probably do when German tanks arrived is get on the radio and ask, “Where are OUR tanks?” – and they were available in large numbers, so they were repeatedly called on to face the German armor. And, not unlike the battlecruisers, losses were heavy.
A Sherman is actually better than a Tiger…for certain uses, like driving cross-country really fast. But the Germans built their late-war tanks specifically to fight other armor, and the Americans did not, so in tank-vs-tank situations, individual American tanks (and their unfortunate crews) were at a significant disadvantage.
The tank destroyer concept was pretty much an American experiment and was more-or-less abandoned pretty quickly after the war. While it seems dumb, remember a lot of countries tried novel approaches in different areas, and some of those paid off…the price of experimentation in tactics and weapons is “sometimes they don’t work well.”
edit: to clarify, other nations had tank-destroyer-like vehicles (assault guns and the like) but were not married to the concept in the way the US was; they were used much like regular tanks.