That's a good question, but here's the catch: feeling better isn't the same as being cured! When you start to feel better, it seems like you've beaten the illness, but what's actually happened is the antibiotic has only suppressed the bacteria's active reproduction. If you stop taking the medication early, the remaining microbes will adapt and start multiplying again - that's called resistance. You'll end up wasting three days of treatment, and the illness will come back, and in a more complicated form that's harder to treat later.
Amoxiclav is usually prescribed for a specific length of time - usually a week or a bit longer. Your doctor calculated this specifically so you can completely get rid of the infection, not just mask the symptoms. If you interrupt the course, you risk the bronchitis turning into a chronic condition or causing complications.
Your friend is giving advice with good intentions, of course, but on this one you really need to listen to your doctor. Trust their prescription and take the full course, even if you're feeling a lot better. When you start feeling really good - that's a sign the medication is working properly, not a reason to stop taking it!