Depends on how you define an asset.
Put very simply an 'asset' is something which puts money in your pocket. A 'liability' is something that takes money out of your pocket.
If you want to be rich then you need to spend your life buying 'assets'. 'Assets' are things where your money works for you and actually earns you more money in the process.
Owning a house which ever way you look at it is a big 'liability'. Think of what it costs to own. Mortgage payments, interest, fees, insurance, DIY, plumbing, decorating, lots of your time - and the biggest cost of all is that it takes money directly out of your pocket that you could have invested elsewhere.
Yes you can argue that houses have gone up in value - perhaps by 100% over the last 10 years. But had you invested is say Gold instead they you would be looking at a 500% return on your money without any of the great expense and hassle that goes with home ownership. That put's things into context doesn't it.
A house will only becomes an 'asset' when 1. - You no longer need to live in it, and 2. - It's going up in value. If it goes up in value but you still have to live in it then it is still just a 'liability'. And its far, far worse now that house prices are on the slide again.
The end result is that despite some of the benefits of home ownership, owning your own home will never make you rich. It's far to expensive in lieu of starting an investment portfolio and sucks too much of your spare cash and time away from buying what could be very successful 'assets'.
There's plenty more good reasons for a house being a 'liability' not an 'asset' in the book but you'll have to have a read if you want to find out more.