My opinion, for what it's worth:
A handicap is an established word meaning an extra challenge. It is entirely benign.
You were taught this/told this. I would question by whom and question whether they were right to teach/tell you this.
The word handicap to me is much less stigmatising than the word disabled or impaired or other awkward attempts to avoid either word.
It seems more fashion, than it is anything of substance.
Though I do agree with the 'has' rather than 'is' grammar distinction that is encouraged.
e.g. "Has bipolar" rather than "is bipolar"
"Has a disability" rather than "is disabled."
"Has a handicap" rather than "handicapped"
Spastic, derived from spasticity, is just a description on the reflexive muscle phenomenon common in cerebral palsy. It was benign but did probably become a slur. Its not a synonym for disabled and inaccurate, so I agree should never be used.