Keep in mind that the CR system is designed to keep battles quick and relatively safe for the PCs. Sure, a party of 4 level 1 players could probably beat a level 2 barbarian with no problem, but that one barbarian could likely kill a player in one hit. Let's say it's using a 1d12 Great Axe and has +3 Strength. With weapon focus, that barbarian hits AC 16 half the time, which some level 1 PCs would be lucky to have. It deals about 10 damage, which would reduce any level 1 PC to less than half health, so it's important for that barbarian to die before striking again. If the barbarian gets a critical hit, that x3 multiplier will outright KILL the PC that barbarian targets, so it's also important that the players have a chance to kill the barbarian before it gets to
attack in the first place.
Also keep in mind, a CR 2 pitted against a first level party is not a common place. Many modules and premade adventures intended for level 1 tend to throw something like 6 CR 1/3 creatures for that kind of challenge, like a pack of wild dogs.
One final note, it's NEVER advisable to send a challenge that relies on class levels unless they outnumber the PCs or the challenge relies on spells. Many equivalent level monsters designed to solo PCs have multiple attacks and better hit points as to make up for the disadvantage of having fewer actions.