Firstly, because it's awful.
But more importantly, given that it only recently gained a university and doesn't have a cathedral (as far as I know) it can't be elected onto the register of cities.
There are some places, for example, Guildford in Surrey or Reading in Berkshire that satisfy both requirements but yet have not been elected onto the register.
The city of Huddersfield in located in the United Kingdom. It is part of the county of West Yorkshire. Huddersfield lies halfway between Leeds, also part of West Yorkshire and Manchester, which is in the county of Lancashire.
Huddersfield Town
Huddersfield is in the Metropolitan Borough of Kirklees, in West Yorkshire, England, halfway between Leeds and Manchester. It lies 190 miles north of London, and 10.3 miles south of Bradford, the nearest city.
Huddersfield, check it if you don't believe me
Northampton Town, Leeds City, Huddersfield Town and Arsenal
Huddersfield Town, Hull City, Norwich. that I am aware of.
Huddersfield's population is 146,234.
It used to be at one time, but I think others may have surpassed it in size in recent years
University of Huddersfield was created in 1825.
Huddersfield Giants was created in 1864.
Per 2011 census population of Huddersfield is 162,949
30 minutes (20 miles on the M62).