Yeah, this person is acting like breaking their concentration on something, to read an e-mail, is drastically different than doing the same thing, for a text. This is a ridiculous assertion. Unless you intentionally make it so you have to log into your e-mail every time you want to use it, but just leave slack, or whatever, open. If you do, that is your fault, not something wrong with e-mail. You can just see e-mail notifications, and then look at the window, just like any messaging system.

This person just has an irrational, personal, dislike of e-mail vs other communication methods. They are trying to make it seem like they have some sort of objective reason for their preference, and it isn't just a personal preference. This way they can try and force everyone around them to bend to their preferences, while telling themselves it is everyone else who is wrong. Like yeah, e-mail isn't the greatest thing around, however it still has some aspects that it does better than anything else, especially in a professional environment. There are rational, objective, reasons most companies still use e-mail, even though they all have slack groups too.