What does the saying, "I don't like to eat what I can't swallow" mean?

"eat what I can't swallow"

as a saying seems to be a nonce. Other than nonsense such as this, I cannot find any other cases.

Searches render suggestions such as these.

When eating food, you first bite off a piece, then chew it, and swallow it. If you bite off more than you can chew, you have taken a bite so large that you are not able chew it. Example: "I went skiing last weekend and I went down the most difficult hill first.

Obviously the reference is:

to bite off more than I can chew

To bite off more than you can chew is to take on more responsibility than you can handle;

-Idioms-online

So,

"eat more than I can swallow"

may be a more extreme paraphrasing of the older saying: i.e. You can chew it, but maybe not swallow. You can bite it, but maybe not eat.

On the other hand..it may refer to

hard to swallow

difficult to believe:

Cambridge online

In other words, he cannot accept the fact.