Why do oxidising agents gain electrons

This may sound reeeeeealy dumb, I know, but.. I'm doing AS level Chemistry and whilst revising I came across the fact that oxidising agents gain electrons. This confused me because, take Cl for example, has a negative charge so therefore has "spare" electron in its outer shell? So surely it gives ITS electron to another species, therefore loses an(some) electron(s). As I said, I'm probably being thick but my Dad is a chemical engineer and agreed with my "logic".
Don't be too harsh on me :P
Thanks in advance!

Cl2 is an oxidising agent to form Cl - .. so Cl - ( a reducing agent)


now.. for the spare electron in outer shell.. you must interprete according to its orbital
like
He - has 1 S2 ( means the first orbital is fully filled - reason why it is inert)

now
for ground state electronic config for Cl atom - [Ne] ( just a short form to make it simpler.)

- [Ne] 3 s2 3p5

so then, truly the spare electron is not actually spare.. when refering to orbitals

the Cl atom gets an e then become a fully filled orbital 3 p 6

Note:
s takes 2 e
p takes 6 e
d takes 10 e
etc..

1st..
reduction means "reduction in charge"... remember that
and
oxidiation is the opposition of reduction.. oxidation is "increase in charge"

2nd..
oxidation and reduction involve moving electrons.
electrons have a "-1" charge..
so..
for a species to be reduced (ie to have it's charge reduced) it must have gained electrons
for a species to be oxidized (to have it's charge increased) it must have lost electrons.

3rd..
oxidation and reduction occur together.
if one species is oxidized, another must be reduced
and..
agents are like assistants... they assist the other species to do it's thing.