Why do batteries only have resistance one way?
To a first approximation, a battery is a voltage source in series with a resistor.
Your wrong impression is probably due to invalid measuring. You can't just connect an ohmmeter across a battery. Most ohmmeters aren't designed to measure resistance with a voltage source in series. That will seriously confuse most ohmmeters.
To measure the internal resistance of a battery, you take two measurements at different voltage and current combinations. For example, you might measure a AA battery when it is putting out 0 mA (open circuit) and 50 mA. You make the assumption that the voltage source in the battery is putting out the same voltage in both cases, and the difference in output voltage is due to the voltage drop across the internal resistance. Then use Ohm's law to find the resistance, but use the change in voltage and current instead of the absolute values:
R = (V1 - V2)/(A1 - A2)
In this case V1,A1 is the voltage and current measured at one point, and V2,A2 at the other point.
You can do the same thing for charging if the battery can take reverse current.
After some time, especially at high current, the chemical reaction in the battery "wears out", and the voltage of the voltage source goes down (or up if charging).
Batteries are complicated, but they don't have resistance "one way", whatever that even means.