What logical fallacy’s are these

Person 1 is arguing from ignorance in both the classic form of argumentum ad ignorantium and complete ignorance of the history of astrology. 

Humans have been charting, studying, developing, and constructing astrological concepts for tens of thousands of years - very likely going back to Neanderthalian dream culture.  Even our modern words for man, woman, moon, menstrual, and month derive from the same early Sanskrit ( Dravidian, Hindu) root. Our original construct of a daily, monthly, and yearly calendar of 365 days aligns with the moon's phases and female menstrual (monthly) cycles.  Moreover, where else did humans witness in spectacular display the monthly transformation of cow horns into a full human face every month without fail? They carefully noted the moon's impact on planting and harvest seasons (as well as the littoral tides). So, there was a widespread belief and burgeoning astrological belief system that developed over thousands of years through Sumerian, Babylonian, Egyptian, Chaldean, Dravidian, Indo-Aryan, Greek, Roman, and Meso American civilizations.  (See The Dream Culture of the Neanderthals by Dr. Stanley Gooch). 

One thing for certain is we do know a great deal about astrology and of all the things we do know (which is a lot) we know it is a completely false epistemology on the same level with haruspicy, alchemy, phrenology, palm reading, and, if we're totally being honest, theology, mythology, and religion itself. 

Beyond the other correct comments on this one, it is also the attempt to prove a negative fallacy.

 Person 2 simply disprove person 1 argument.

"Person 1: So just because  we can’t explain Astrology yet doesn’t mean it’s been disproven. So you don’t know then! Science has been wrong before. " . At most it would be unproven but consider what was the first statement I would call it biases.

"Person 1: Well maybe astrology is True we just don’t know yet . " would be an opinion.