Why does fluorine stabilise a carbocation? I have read that halogens have a stonger -I (inductive effect) than +M (mesomeric effect),then why do they stabilise a carbocation instead of destabilising it?

I asked this doubt to my teacher and he said that halogens like fluorine do not exert -I on a carbocation and hence they stabilise a carbocation through +M,is this true?
Fluorine belongs to the same period as carbon. Carbocation is electron deficient which has its two $\mathrm{2p}$ orbitals vacant. One electron of carbon in $\mathrm{2p}$ orbital goes into the formation of $\ce{C-F}$ σ bond. $\ce{F}$ has $\mathrm{2p}$ orbital containing a lone pair which can be donated to the $\mathrm{2p}$ vacant orbitals of carbocation. Same size $\mathrm{2p}$ orbitals of carbon and fluorine overlap effectively to form a π bond.