I need help understanding the different acid/base theories like Lavoisier, Davy, Arrhenius, B/L
I know the main definition but need help on the disadvantages of each theory. Thanks 
For the acid-base theories, the disadvantages are essentially what is
not addressed by each theory.
Lavoisier stated that all acids contain oxygen. Counterexample: HCl.
Davy stated that all acids contain hydrogen. Counterexample: NaHCO
3.
Arrhenius stated that all acids ionise in water to produce H
+. This was quite an improvement from theories in the past and is quite accurate. He also defined degree of ionisation, as well as taking the concept over to bases as well, claiming they must contain OH
-. This also lead to the concept of neutralisation.
The counterexample to this one is mostly with bases. Again, NaHCO
3 is a counterexample, but for a different reason. It's a base that doesn't contain the hydroxide ion.
As far as things go, modern day acids and bases are always defined based off B/L theory. At least, that's the convention, and how HSC goes. In reality acids and bases are categorised into two types: B/L and Lewis acids/bases. But you do not need to go any further - take it for granted that B/L is the most accurate of the lot. It also has the ability to address the amphiprotic nature of substances as well.