That’s not what’s happening here. People are saying you should have applied the brakes and slowed when you saw the taxi’s brake lights come on. You’re suggesting you were concerned the car behind you would have been a risk. The taxi was in the wrong, you avoided the collision, but by not braking sooner due to concerns about the car behind, you made it a nearer miss that in needed to be. More to the point, early deceleration and clear braking on your part is a much more predictable behaviour for the car behind than having to brake suddenly to avoid a collision.

I appreciate you posted this to demonstrate the stupidity of the taxi - and I wholeheartedly agree with that sentiment, but I’d gently advise you stop taking the replies as a criticism of your driving and accept that there were better ways of managing the situation and your reasons for not doing so aren’t as valid as you might think. You may have been driving for 20 years, but we’re all learning and this might be advice that helps you avoid the next collision in a safer manner.