a classic endgame
I disagree in a nice way. It has long been known that a draw offer can have an adverse effect on the player who is winning. They can have a tendency to overpress and if things don't go their way quickly, they can blow up. Practical chess tips often give examples of 'the psychological draw offer'.
we seemed fairly evenly matched for most of this, and i daresay we both made errors of judgement, but a point arrived where he declined my offer of a draw, so i decided to make my extra pawn count.
after the queen exchange, the extra pawn quickly became decisive, and careful classic end game theory worked like a charm.