They are false gods because they are made up (a false teaching)!
I think you're missing the point. There are no other gods! Any belief in another god is a false belief. The god of such a false belief is therefore a false god.
Deuteronomy 32:39
Look now; I myself am he! There is no other god but me...
1 Kings 8:60
Then people all over the earth will know that the Lord alone is God and there is no other.
Isaiah 43:10
...There is no other God—there never has been, and there never will be.
You're reading from the King James, which has translated this scripture badly. There are no gods (plural) in this scripture. It says that they will be as God (singular), and every other translation of the bible renders it this way.
“God knows that your eyes will be opened as soon as you eat it, and you will be like God, knowing both good and evil.” (NLT)
“For God knows that when you eat from it your eyes will be opened, and you will be like God, knowing good and evil.” (NIV)
“For God knows that in the day you eat from it your eyes will be opened, and you will be like God, knowing good and evil.” (NASB)
for God doth know that in the day of your eating of it -- your eyes have been opened, and ye have been as God, knowing good and evil. (Young's Literal Translation)
that one-knowing Elohim that in day-of to-eat-of you from him and they-are-unclosed eyes-of-you and you become as Elohim ones-knowing-of good and evil (Interlinear Hebrew to English)
We don't know exactly who the "us" is in this scripture. The only thing we know for sure is that it is NOT "other gods". It is possible that the "us" refers simply to angels (who reside in heaven with God, and who would know good and evil by then).
What translation are you using? Deut 32:39 says He has no God WITH Him. More literally, it says no God AGAINST Him. Much different. I can see why some translaitons have to change it to say "but" me because they recognize the original text conveys there are still other deities in existence. May be related to why the Masoretic text changed Deuteronomy 32:8
"And there is no god with Me".
With. Not But. With.
1 Kings 8:60
for all the peoples of the earth knowing that Jehovah, He is God; there is none else;
This simply means that they will recognize he is THE god. The article is there for a reason. "The god" does not mean there are no other beings called gods. It means he is THE god, "The god of the gods" as he is called elsewhere.
Isaiah 43:10 says no god BEFORE which means "more important than" and "After" which can mean "like or similar to".
The translations that you are using deviate from the literal text to apply a pure-Monotheistic spin to it. The original Israelites were Henotheistic, not "Monotheistic". The Septuagint of Deuteronomy 32:8 confirms this, as the Masoretic is most likely a later change.
Angels are in fact called "gods". They are not called "false gods" or implied as "false gods". They may not be THE god. But they are still "gods". It's important to understand what the concept of the article before "god" means.
There is no reason to read it as "You will be as God" instead of "You will be as gods" in Genesis as well. Except circular reasoning. The word "Elohim" doesn't always ever mean just "God" and often does in fact refer to the literal plural.
And as I said, the "us" in 1:26 is most likely referring to the Angels, who are in fact called "Elohim".
Hope that helps.