The main objection to computer-aided proofs is not that they are more difficult for humans to understand.
The main objection is that most proof-assistants use a different logical foundation than modern mathematics. Modern mathematics is built on ZFC[0] whereas most proof assistants, such as Coq, Isabelle, Agda, etc use different logical foundations, such as the Calculus of Constructions[1].
Many important results in modern mathematics are not easily stated or proven in systems such as CoC[1]. For example, Brouwer's _Fixed Point Theorem_[2], a pretty bog standard result in Topology that is useful to proof many things in Functional Analysis, has a clear statement in ZFC, but does not, to my knowledge, have an equivalent in CoC (and if it does it will be stated radically different).
The main objection is that most proof-assistants use a different logical foundation than modern mathematics. Modern mathematics is built on ZFC[0] whereas most proof assistants, such as Coq, Isabelle, Agda, etc use different logical foundations, such as the Calculus of Constructions[1].
Many important results in modern mathematics are not easily stated or proven in systems such as CoC[1]. For example, Brouwer's _Fixed Point Theorem_[2], a pretty bog standard result in Topology that is useful to proof many things in Functional Analysis, has a clear statement in ZFC, but does not, to my knowledge, have an equivalent in CoC (and if it does it will be stated radically different).
[0]: https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_t... [1]: https://en.wikipedia.org/wiki/Calculus_of_constructions [2]: https://en.wikipedia.org/wiki/Brouwer_fixed-point_theorem