"Handicap began to be applied to physical and mental differences in the early 1900s, when the new fields of sociology and social work started looking at people in terms of their place in society as a whole. What had been seen before as individual failings or flaws were recast as disadvantages with respect to larger contexts. If life was a horse race, a person with a physical disability couldn’t compete as well because of the burden they had been handed, not because they were defective by nature. Over the next decades, old words that cast disabilities as personal flaws—crippled, lame, imbecile, invalid etc.—became increasingly offensive sounding, and by the 1970s, handicapped had become the term of choice in social services and legislation."

Handicapped came onto the scene as a PC term, so you're not incorrect.

As for "disabled", its etymological form means “rendered incapable,” not a very liberating sentiment, and it had a history of being used to describe disabled people going back 200 years before "handicapped" became common.

https://www.etymonline.com/word/disabled

Basically, it's a personal choice to be offended by the word.