It's because the right side is "loaded" after you throw a left of any kind (hook, jab, etc). Your weight is firmly on your right foot now and your right shoulder is cocked back. You could start from this position without throwing a left first, but it might be telegraphed-- pulling your arm back, etc. is a common tell that makes shows that you're going to throw a right (looks kind of like in those old John Wayne cowboy movies). Or maybe you could just move around and keep this position as your default, but they'd still know that was your main punch you were meaning to throw and would be waiting for it.
Same thing happens to your left side after a punch from your right. All the weight goes on the left foot and is loaded for a really nice left hook. This is why combos and feints are nice, they conceal the powerpunch thats about to happen and load the spring (your leg). If you want really exaggerated and easy to see but also technically correct examples of this, watch Mike Tyson footage on youtube (especially in slow mo they usually re-show after the KO). He really loads up and gets a good bend into his leg before letting it go.
