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Selling puts is not a short at all

It is commonly referred to as a ‘short position’, though it is not ‘shorting the stock’. Equally, purchasing calls* is referred to as a ‘long position’ (as is holding the equity).

edit: smallmancontrov below pointed out that I wrote 'purchasing puts' was long, when I meant to write 'purchasing calls'

Selling puts is a long position. Purchasing puts is short.

It’s all a matter of perspective I suppose, and of course I understand why you say this, but no professional options trader I’ve ever met would speak in these terms.

Buying puts.

Once you fully risk manage a short position and account for the price of doing so, you might realize that you have reinvented a put contract.

They’re buying puts.