I think what I'm having a hard time understanding is Ohm's Law in regard to pulling current. If a power supply CAN offer a certain amount of amperage, why doesn't it?
Think of a garden hose attached to your garden spigot. Let's say 1 gal/min flows out. Now partially block the hose with your thumb. That might reduce the flow to 0.5 gal/min. Your spigot is capable of supplying 1 gal/min but the hose is now only able to deliver less. Squeeze tighter and the flow decreases further.
Current behaves a lot like flow; voltage is a lot like pressure. Your spigot is roughly a constant pressure (constant voltage) supply and can only push as much flow (current) as can flow through the load - your thumb or the circuit.
If the city turns up the water pressure while you're doing this test, the flow past your thumb will increase. The same thing happens electrically if you increase the voltage and this is what Ohm's law is about.
You may be thinking about power supplies as if they were constant current supplies. There are such nthings but most are not. Constant current supplies are special purpose supplies that work by sensing the current they are supplying and actively adjusting their voltage as necessary to keep that current at the set value. A battery, your wall outlet, or a USB port power supply are more typical of constant voltage supplies. (I'm waffling about the constant voltage part because simple power supplies don't actively maintain their output voltage; as they supply more current their voltage decreases. Usually only sightly as they supply low currents, but more, as they approach their maximum capability.)
doesn't that mean there is no constant?
Yes, literally speaking. But a simple power supply such as a battery behaves more like a constant voltage power supply than it does like a constant current one, if the current draw is within its capability. And don't take "constant" too literally. A 5v USB supply might be a couple tenths above 5v with no load and drop a few tenths for typical loads, more for loads that draw more current, and in some cases, like my iMac's USB ports, may go to zero - disconnect - to protect themselves and the computer, if the load tries to draw too much current.