Your toddler may be able to walk short distances around your living room like a champ. But send him out into the hustle and bustle of the real world, and he won't be able to keep up the adult pace for long. He simply can't move his little legs fast enough, let alone for more than a few minutes — and trying leaves him exhausted (and you frustrated). Plus, it's uncomfortable for him to keep his hand raised high in the air to hold yours.
Until he's around three years old, he'll probably need his stroller most of the time. You can also try making the idea of walking a game, where it's a trade-off: If he walks to a set landmark, he can sit in the stroller until the next landmark and so on. Just make sure you praise him — especially now that you know how hard he's working!