Where Marxism fails is when it behaves like a religion. First of all, it makes itself unfalsifiable. Point out the failings of any given socialist country and all you hear is "if they had just *implemented it correctly it would have worked!" It's no different from saying if we had a caliphate with true sharia everything would be perfect. True sharia isn't defined, the only criteria for 'true sharia' is that it would create a utopia - because they circularly assume sharia would have to do that. Same thing with Marxist thought in many areas.

The next issue is the holistic nature of it. Marxism doesn't stop at economics. You have 'historical materialism' which purports to explain all of history - not just economic issues in it, everything - through a Marxist lens while also providing a predestination narrative - the "inevitable" transition to communism in the stages of economic eras. Marxism tries to shoehorn everything into a framework of class struggle. Class and wealth distribution do affect everything, but Marxists usually try to say that every problem has it as the root. You may have heard Marxists who claim that ideologies like religion, nationalism, racism, etc are actually a secondary or tertiary result of economic issues, or that they are directly engineered by a mystical bourgeoisie which is somehow immune to them. It's denying the agency of the actual people involved, people who do sincerely hold the beliefs they do. You can think of the wealthy Saudis who run Islamic charities and try their best to spread Wahhabism around - it's not because they're making any financial return by building mosques and feeding people in poor countries, they are doing it entirely because they believe they will help these people on a spiritual level.
When you try to take complex, interconnected systems like religion - where very many factors are at play - and try to say it's ALL due to one factor, you're gonna get it wrong. For instance, the Soviets were surprised religion didn't go away once they had a socialist system - because they fully believed religion was just a tertiary consequence of capitalism and would disappear naturally. They couldn't see things outside of the class struggle.

Another issue related to the above is that it's all self-contained. Not only does Marxism attribute everything to a few issues, Marxism itself contains the answer to every given problem. Marxists tend to be quite proud of this "all-encompassing science" but that aspect always troubled me.

And finally, it uses the simplified social theory to create an us vs them narrative - you always need a simplistic worldview to have "good guys" and "bad guys."
When you add it all together it's just so much like a religion