It's rude, it's offensive, it's more offensive than no invitation at all. If you are tight on numbers, it's less offensive to invite a couple just to the evening than him to the day and her to the evening, or not at all, few people feel they must be invited unless they are a sibling of the Bride or Groom!
If you really can't fit everyone in, then don't invite them.
It's also showing a lack of social grace and understanding to think that the "plus 1" is just there for you - it's amazing how many people on here think it's ok to say "well, I don't know the husband of X so I didn't invite him" because your enjoyment of the day is the sole priority - having a guest with them, someone to acompany them for the day is actually about being a good host to the person you have invited. It's unlikely, with a wedding with a lot of guests, that you can spend all day chatting with a friend, so having a 'date' with them is showing consideration to their needs. Not everyone will bring their other half or indeed a date at all if single, but turning up alone to a whole day event where your host will not have much time to talk to you is hard to do for the bulk of the population.
A wedding ceremony is about the couple. A wedding reception is a party the couple have hosted, being a good host means you do have to think about the needs and comfort of your guests. This normally would include giving them the opportunity to have their partner with them.
If you really think it's "all about us" then don't have any guests! If you want to throw a party as well, then throw a good one. And good party hosting involves not being a dick towards your guests. You can have the best flowers, the most amazing band, the most fabulous food, but if everyone's having a shit time, it won't matter, it'll still be a really crap wedding.