Colin to answer your question, I do not really have a reason, I'm just curious about it. Maybe one reason would be that it would be (a little) harder (for me) to match them.
Is it bad if my capacitor is 100 times larger than it needs to be (ignoring losses), when we're talking about a part that costs less than a cent...
Or is there another reason to match the parts; that's maybe where i'm getting at.
To be fair, too, I'm not actually a total beginner and I do understand inductors and capacitors fairly well I would say.
I do see too what Ratch is saying about circulating currents.
I feel that we got a little hung up on this technicality, but I might as well add my two cents:
The current does not technically oscillate, of course the energy does.
Inductor: Likes to keep current flowing through it constant at all cause and will happily inject a voltage to keep current going.
Capacitor: Likes to keep the voltage constant at all cause and will happily inject a current to keep the voltage the same.
This btw. is what I meant with "magic". The mirror like features between capacitor/electric field and inductor/magnetic field. It's like ying and yang right?
During the oscillation, all the energy exists in the form of an electric field in the capacitor (voltage). The voltage is driving a current through the inductor. The capacitor wants to keep the voltage up and is injecting more current, which flows through the inductor. Eventually the capacitor is depleted and there is a point when there is no voltage on the circuit and now all the energy is stored in the form of the magnetic field in the inductor (current). This must be the point where voltage polarity switches. Now that the capacitor can no longer push any more current, the inductor is creating a voltage, trying to keep the current going (while eating up it's magnetic field), and this in turn charges the capacitor again.
So yes, energy definitely goes back and forth, switching between voltage and current; and yes, there is always some resistance and other losses (including the radiation of energy) which dampens this oscillation; and of course in any practical example we also need some type of driver to keep topping off the circuit (just like a swing set) to keep things going.
One thing I would add. The energy, voltage, and current all oscillate. I will modify what I said about mismatching the L and C. As I said before, as long as the product of L and C are the same, the resonant frequency will be the same. If you increase L and lower C, the impedance of the tank circuit will increase and the circulating current will be less. The opposite will be true is L is made smaller and C increased. Therefore you can adjust the circulating oscillating current by fiddling with the L and C ratios as long as you keep the product the same.