Why Won't My Cat Let Me Cuddle It?

These are horrible answers these people made.  

Here are my answers by experience, training and research:
Your cat is not used to touch first of all.   So ease your cat into the capability of beng touched.   Pet her on her back when she eats.   Pet her on her back slowly about two times when she plays and pull your hand away so she doesn't attack you.   Pet your cats nose with 1 finger softly while she naps and as time passes pet her head.  

Never Pet your cat on her belly while she is on her back.   This makes her feel trapped.
Never Pet your cat in front of her chest, belly, or face while she is in play mode.
Never straight up grab your cat and hold her in your arms right away.   Naturally cats feel this as entrapment and will do what they can to get out of it.  

When you are sitting on your computer pick your cat up and place her in your lap with 2 pets to her head or back.   Then let her be.   She will firstly jump off because she isn't used to that environment.   This has to be a consistant routine each day so your cat understands that you are allowing her to be in your territory.   After time she will understand and realize, your lap is a safe zone.

The short answer to this is : because it IS a cat ! Cats are notoriously 'picky'. It probably knows that you want to cuddle it, so it won't let you do this.
It may be that the cat was never handled properly when still a kitten and so it never felt comfortable being handled. Now it has translated this into 'I don't do cuddles'.
Cats are all individual and unique and we cannot train cats (which is one of the reasons why we love them), so this situation is likely to remain unchanged.
You could, however, turn the tables a little. If your cat is not affectionate and is indifferent. be the same, just ignore him/her a bit more, do not try to pick him/her up. Try this for about a month and you may find that the cat is a little more demanding of love and attention..... but on the other hand, you may not !

Let the cat come to you and feed it by hand and be very nice and calm. Do not make quick movements.