At one end, people are upset because the characters receiving the mantles were wholly and solidly established as their own characters, and the mantle they're given overshadows that. Consider, for example, the decision to "kill" Captain America and have Falcon take the mantle. Falcon had, by that time, been fully established as his own person with his own dreams, wants, and desires. Then he got saddled with Cap's legacy, and his entire nature as an independent character got shoved out the window; instead, his new character is "replacement for previous guy".
At the other end, people are upset because the replacement characters aren't adequately sold to the public. For example, whereas in the MCU Peter Parker became Tony Stark's heir because he'd been Stark's student and was one of the most logical successors despite his inexperience, in the comics Riri Williams is a teenage wunderkind who was the most awesomest student ever at MIT, such that Stark didn't even mind her stealing the college's equipment to make her own armor because he was that magically impressed with her; when he went missing, all she had to do was prove how big a fangirl she was and she was in. This at best came off as her being somebody's wish fulfillment character, and at worst came off as a ham-fisted attempt to shove Stark aside for someone more "woke".