Stainless comes in lots of different grades. What grade did you use?
Some stainless (like 440C) can be harden and tempered and is used for knives. If you use this type of stainless then in the act of drilling, especially because of the thin tube wall, you probably hardened and air cooled it (rapidly) hence you could produced a tube that is harder than your tap - this is the most likely outcome if you haven't used flood coolant and cutting drill oil.
Other stainless (like 304) does not harden but like all stainless it does not like heat. A product of the heat is that the stainless expands and clamps your tap - which restricts the hole, which clamps tighter on the tap, which creates more heat as you force the issue..... until either the metal and tap binds or one simply degrades to the point of useless. (alternatively if you get away with it you get an odd dimension hole)
...
T
Two ways to get hardness - work hardening and heat treating - totally different.
304 (300 series stainless) cannot be heat treated to get hardness, as Tom says, but it
will work harden (or strain harden) enough to give you significant trouble machining or tapping if you don't do it right. 400 series are martensitic and can be heat treated to significant hardness hence their use in knife blades, etc, as Tom says, and they are easier to machine. If you search the professional machining forums you will see overwhelming complaints about machining, tapping, 304, 316, etc because of the work hardening characteristics - broken tools, overheating, dulling tools. One guy even said 304 was a "design error." (I liked that) It's generally all because of technique and close attention to "making the cut right." I'd stay away from 300 series for pen making if I could unless that's all the material I had and I wanted to gain more experience cutting it.
IMHO I can't think of any real design reason to make a pen out of 300 series stainless unless you want to make one out of some of the really pretty Damascus steels such as what is made by Damasteel.
Unlikely you will be able to rethread with a carbide tap but maybe you can get it to work. You can, however, anneal the stuff:
if 300 series - heat red hot and let cool any way you want
if 400 series - heat red hot and let cool very, very slowly (like a few hours or more)
if you don't know - heat red hot and let cool very, very slowly (like a few hours or more)
You will likely have your work cut out for you re-finishing your surfaces after that.
Good luck - I hope you can fix it!