Exaggerating the importance of outliers, or overinclusivity

A problem of definition that sometimes arises is when people try to be overinclusive, and try and include the outliers in the definition in order to change the definition. An example could be:

"Humans have 5 fingers on each hand, and 5 toes on each foot"

"Well some people have polydactyly, and some have birth defects, so to be exact, you have to say that humans can have anywhere between 8 and 12 fingers in total"

This is not about anecdotal evidence, but the point here is that the outliers are so rare, that's it's not worth including them in the definition, or the definition would become so broad as to basically be meaningless. This is also different from the appeal to definition, because here an active attempt is made to disregard the dictionary in favor of completely changing the definition to benefit the arguer.

What fallacy would this be? Or is it a new one?

This isn't an argument; it is just being pedantic . Take your example statement:

"Humans have 5 fingers on each hand, and 5 toes on each foot"

It is well understood that if a human loses a finger in an accident, they are still human. There is an implied "generally" in there that we all understand. It is so well understood, that adding the "generally" is unnecessary. So if someone counters with "not exactly,..." they are just stating the obvious, or being pedantic. We all want to slap people like this.

I am not even sure how to make this a credible argument (an argument that someone might actually make) to look for a fallacy.

EXCLUDED MIDDLE: To wit, "SOME humans have MORE than 5... SOME LESS than 5..."

"Humans have 5 fingers on each hand, and 5 toes on each foot"

Nowhere does this say 'can only have five fingers.....' etc....

This is a contextual issue. In a general, informal, context, then yes, humans have five fingers. In a deeper discussion, the definition must be more specific.  This illustrates why  the definitions are important to a discussion and all participants must agree on the meaning of the definition in use for the particular discussion.