That’s what the lyrics say though.
On the X day of Christmas my true love gave to me, X [item], X-1 [item], etc.
The song explicitly states they give this stuff every day.
Only if you take it literally and I don’t think it was intended to be taken that way.
“on the second day of Christmas my true love gave to me, two turtle doves and a partridge in a pear tree.”
It takes a bit of mental gymnastics to assert that on the second day of Christmas he did not send two turtle doves and a partridge in a pear tree.
If I said yesterday I gave my friend a pork pie and today I gave my friend some spaghetti and a pork pie, you would not come to the conclusion that my friend did not receive a second pork pie.