Why is it some adjectives don't seem to accept negative prefixes and only are used with the negative adverb "not"?

Solution 1:

First, it's not very accurate to say that un- is applied to words of Germanic origin. Many adjectives built on Latin or French bases can be prefixed with un-, such as unpleasant, unrealistic, unlimited, unconditional, uncomfortable, and hundreds more. I wrote an answer with some other examples here. It's more accurate to say that the negative prefix in-/im-/ir-/il-/ig- occurs exclusively with words of Latinate origin, whereas un- is possible with adjectives of any etymological origin, but especially productive with adjectives with certain endings (such as -ed or -ing).

As you've observed, un- cannot be added to all adjectives. There's no simple explanation for it that I know of, so it's just something that I would say needs to be memorized. Googling the topic led me to a 213 page disseration on the topic, "Creative prefixations and the prefix un-: A cognitive linguistic analysis", by Balázs Bernadette (2016)–I only skimmed it, but the length and the parts that I did read are consistent with my guess that there is no simple answer to why unangry isn't typically used.