Updated:

1. Build a glass arena

/fill ~5 ~-1 ~-6 ~17 ~4 ~6 minecraft:glass hollow

hollow builds only the outer shell, so you can watch safely from outside. See the fill command.

2. Summon the fighters

/summon minecraft:zombie ~8 ~ ~ {PersistenceRequired:1b,Tags:["red"]}
/summon minecraft:skeleton ~14 ~ ~ {PersistenceRequired:1b,Tags:["blue"]}

Skeletons burn in daylight, so run /time set night first.

3. Start the fight

/damage @e[tag=red,limit=1] 1 minecraft:mob_attack by @e[tag=blue,limit=1]
/damage @e[tag=blue,limit=1] 1 minecraft:mob_attack by @e[tag=red,limit=1]

Each mob now thinks the other attacked it and goes after it. See the damage command.

4. Team battles

execute as @e[tag=red] at @s run damage @s 1 minecraft:mob_attack by @e[tag=blue,limit=1,sort=nearest]
execute as @e[tag=blue] at @s run damage @s 1 minecraft:mob_attack by @e[tag=red,limit=1,sort=nearest]

Every mob targets the nearest enemy on the other team.

5. Show the winner

execute unless entity @e[tag=red] if entity @e[tag=blue] run title @a title {"text":"Blue wins!","color":"blue"}
execute unless entity @e[tag=blue] if entity @e[tag=red] run title @a title {"text":"Red wins!","color":"red"}

6. Natural enemies

Troubleshooting

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