Why did someone on BBC Breakfast say that a second referendum was an attack on Democracy?

It depends on the wording. It is notable that nobody who wants another referendum can say what they want it to be about. If it is a repeat of the previous one, then we've already voted on that and it's an attempt to bore us into submission until we come up with the "right" answer. A typical tactic of the illiberal left.

If, on the other hand, it is a referendum on something else, such as the terms of leaving, that's different.

Special interest. Baron Von Arnheim, shortly before he passed, advised them to invest very heavily in Brexit.

Because they voted leave and know that the polls show that another referendum would result in the majority being in favour of remaining.

If one holds a "binding" Referendum on a particular issue ,then for the losers to argue that there should be another Referendum ,on the same issue , just in case some people have since changed their minds -- is an affront to democracy .

Only the "left" believe it is "democratic" to accept only those election results that agree with them --and "fair" to reject all others results.

Simpletons are allowed on the BBC.

In Switzerland, they don't keep holding referendums until they get the result they wanted.