Why don't we use beta radiation to make our electricity? Since it is an electron being released/made, it would make sense to try and capture it. But, we obviously don't so. What am I missing in my logic?
From what I understand from the Wikipedia article on atomic batteries, the problem is not a physical, but rather a technological one: The currents are too low, the voltages too high and generally those contraptions have poor efficiencies.
Additionally, in general you want batteries to deliver a more or less constant voltage independent of the charge condition - this is what distinguishes good batteries from cheaper ones. You can imagine that a battery using a radioactive source will show a voltage drop somehow proportional to the decay of the isotope powering it, which is an additional unwanted characteristic.
The thing you are thinking about is something called 'direct charging generator' in the article:
Direct charging generators
(...) Although this form of nuclear-electric generator dates back to 1913, few applications have been found in the past for the extremely low currents and inconveniently high voltages provided by direct charging generators. Oscillator/transformer systems are employed to reduce the voltages, then rectifiers are used to transform the AC power back to direct current. (...)
I suggest you also check out the article on betavoltaics and references therein - those describe a more sophisticated approach to this technology using semiconductors.
We do use beta radiation for electricity production. In a typical fission reactor beta decay of fission products provides about 6% of the reactor power. As other types of radiation it is converted to heat and then to electricity. This energy is also the source of decay heat in the reactor.
Since this energy represent a small amount of overall power there is no engineering reason to try to convert this energy directly to electricity.
Beta radiation is used for electricity production. Devices that do this are called betavoltaics. Because of their low current output, they are only used for things that need a very small amount of power for a very long time. They are frequently used as "batteries" for things like spacecraft going far away from the sun, and used to be used as a power source for pacemakers.