Why is the Arabic word جید (jayyid) which is pronounced gayyid in Egypt and means good, so similar to the word good or the German word gut? Is it a borrowing? (since the word for good is very different in Hebrew - it is טוב (tov)) If it is a borrowing, why would such a basic word have been borrowed by a people?
I was only able to find the Arabic word ṭayyib (طَيِّب) meaning "good".
The word is a cognate to Hebrew tov (טוֹב) comes to the Proto-Semitic ṭayb and further etymology is unavailable.
The etymology for the word you mentioned is unavailable, but I want to put out that the spelling usually indicates the former pronunciation. This means that if the word was borrowed, it was starting with j- at the time rather than with g-.
The English word "good", related to Russian "годный" "suitable" comes from Proto-Indo-European root ghedh- which means "fit together". I do not see any connection.
"جيّد" [jayyid] (having quality; refined) is an adjective from "جودة" [jawda] (quality), so there is a
[dʒ] not a
[g] in the beginning of the word but in the Egyptian dialect of the Arabic language the
ج is spoken as a
[g] giving the sound
Aftermaths, no borrowing from the Egyptian dialect regarding the word "good" or "gut".
A quick search of جید on Google returned two relevant results.
The first one is a pronunciation of the word by an Egyptian speaker, where it is pronounced with a plosive-velar [g]. the second result is a Wiktionary entry of that word where the pronunciation is with a velar [j].
Given the fact that Arabic has many (many!) dialects, it's not surprising to see a word, even a "basic" one, being pronounced differently in different cultures and societies. In fact the difference only in the manner of pronunciation indicates that one of the consonants is an allophone of the other and not a case of borrowing the whole word.
The close relations to Hebrew can also help to shed light here, the Hebrew word for good טוב (tov) is very similar to the Arabic word tayyib (طَيِّب) which also means good, and from there the jump to jayyid or gayyid is not very far.
I might not be a professional, or any sort of authority in this matter, but it seems to me that a language borrowing a single word is less likely do so if the word already exists in the borrowing language, especially a fairly common and "basic" word like good.