How can I delete just one occurrence of a recurring event without changing the whole series?

This would be ab EASY FIX.

What the OP and others here are suggesting (I'm guessing) is that - while the cause may well have been what N. & B. have posited - the described solution is a helpful BandAid but doesn't address the desire for a practical, permanent fix.  If two options are already offered to edit a series of recurring calendar events, might the experts at Google consider adding one more to simplify the task of changing just one day's event without affecting the entire series?

So whatever is happening here, it is NOT a missing third option that could be added, the problem is that this third option is REMOVED because for whatever reason it can not be applied to this event.

The problem with editing event series is that "deleting" will never actually remove any data - to the contrary: it will ADD an exception to the series!

Example:

You create a daily event for the month of May. What is stored is: "Dinner at 8pm daily from May 1st to May 31st". Now you try to delete one of those, or so you think. What happens is an addition: "Dinner at 8pm daily from May 1st to May 31st except for May 15th".

Instead of deleting, you now have to store more.

Making edits for single or "for this and future" events works the same, just worse.

tl;dr;:

I'm in no way surprised when editing repeating event doesn't work as I expect it to.

Then you select the first occurrence after the one you amended and change it back to the initial settings and click "save" - again choose "this and following events".

If you want to delete one instance of an occurring event, you select the occurrence you want to delete, make a random change (do NOT delete at this stage), click "save" and choose "this and following events".

After you performed this action, you again choose the instance you want to delete and choose "delete" - if you then click save you will get the option "only this event".

It's a bit circuitous, but it works.