This is true only one day in a year.
Its December 31st
It is 31 Dec, Suppose you are asking on 1 January 2014 so day before yesterday means 30 Dec 2013 he was 25 but on 31-Dec-2013 he was 26 and as on this year (2014) on 31 Dec 2014 he will be 27 and next year (on 31 Dec 2015) he will be 28 year old and its the solution
He was born on December 31st and spoke about it on January 1st.
Phil asks his friend Stan when his birthday is. Stan replies that he was 32 the day before yesterday and next year he’ll be 35. When is his birthday and how is this possible?
If the day before yesterday Susie was nine, yesterday she was ten, and next year she will be twelve, when is Susie's birthday and what is today?
Joe said to his friend at a New Year's Eve Party, "Yesterday I was twenty, but next year I will be twenty-two." When is Joe's birthday?
