Because the proof is flawed, why do people still bother with it? if you do it with numbers, it doesn't work but if you do it with letters then it kind of does, until you realise that you are dividing by 0.
Exactly so it's showing the original theory was wrong. The saying 'works in theory but not in practice' is actually nonsense because if it doesn't work in practice then the theory was wrong - as in your case because you can't divide by zero.
For the benefit of those who haven’t seen this ‘proof’ before:-
a = b [multiply by a]
a^2 = ab [subtract b^2]
a^2-b^2 = ab-b^2 [factorise]
(a+b)(a-b) = b(a-b) [divide by (a-b)]
a+b = b
I recall that my maths teacher could not find the flaw in the above equations.
But then it was a secondary modern comprehensive school – the main purpose of which was to provide adult employment for those who would otherwise be unemployable.