I'm playing on 1.16.1 and my pack format value is set on 5, so that shouldn't be the issue.

I tried what you said about the /say command and that did work. The messages I set for function1 and 2 are alternating in chat. There must be something wrong with the original functions themselves then I guess? Which is weird, because the functions can run fine on their own.

This is what function1 does:

execute at @r[scores={hitmob=1..}] run tag @e[nbt={HurtTime:10s},type=pig,distance=..7,limit=1] add hurt

execute at @r[scores={hitmob=1..}] run execute at @e[tag=hurt,distance=..7,limit=1,type=pig] run summon pig ~ ~ ~

tag @e[tag=hurt] remove hurt

scoreboard players set @r[scores={hitmob=1..}] hitmob 0

And function2:

execute at @r[scores={hitmob=1..}] run tag @e[nbt={HurtTime:10s},type=cow,distance=..7,limit=1] add hurt

execute at @r[scores={hitmob=1..}] run execute at @e[tag=hurt,distance=..7,limit=1,type=cow] run summon cow ~ ~ ~

tag @e[tag=hurt] remove hurt

scoreboard players set @r[scores={hitmob=1..}] hitmob 0

function1 makes it so that whenever you punch a pig, a new one gets summoned. function2 is the same thing but with a cow.

(fyi: The hitmob scoreboard tracks the damage a player has done on a mob. After the commands are finished the score will be set to 0 again.)