Because unless specifically requested, the usual attire for males to wear at a funeral to show respect for the family & friends of the deceased is a dark suit/shirt/black tie/black smart shoes, all clean and tidy. If you haven't got a suit, if possible get one. If you can't, at least make what you are going to wear to be clean and tidy and preferrably a smart shirt/tie trousers and jacket combination. Trainers/jeans/t-shirt and any form of casual attire can come across as being disrespectful, especially if not clean and worn in a scruffy way. It doesn't automatically follow that it will, but wearing the more usual suit combination generally avoids any unintentional offence being caused.
Attending a funeral isn't necessarily about YOU, it's about everyone else there, in particular the closest family of the person that has died.It's about showing RESPECT for the life of the person who has died and his/her memory to the closest family & friends of that person, as a funeral is a way of saying goodbye and marking. One of the ways we show respect is by the clothes we wear.
Also think on this - is your wife feeling sad/stressed about the death of that person - if so, why risk increasing her sadness by getting her even more stressed by worrying what you wear or don't wear? Would it really be so hard to put a suit on for a few hours on one day? Funerals are one of those times in life where stress is bad enough already without unnecessarily increasing it.