While you can use the funds in an HSA at any time to pay for qualified medical expenses, you may contribute to an HSA only if you have a High Deductible Health Plan (HDHP) — generally a health plan (including a Marketplace plan) that only covers preventive services before the deductible. - healthcare.gov
To give something that is or becomes part of a larger whole. - contribute, wiktionary
Putting in money to my savings account does not give money to become part of a larger whole. I know that Health Savings Account is tax-free savings account for the account owner's medical expense. It is not to donate or make part of public fund.
Why do you say 'contribute' instead of 'deposit' on HSA?