Not buying a house may decrease mobility for some, especially single people. But folks who have spouses and/or kids tend to be more anchored to the community regardless of whether they rent. They have jobs and schools and friends that are hard to move away from.

Also, buying a house can be an opportunity itself. Although the new tax law makes it somewhat less tax-favored as an investment, it still offers the ability to escape capital gains taxation on up to $500k (married) of gains. There are other federal and state benefits that can make the overall purchase decision attractive.

So for some folks, yes a house can be an anchor. For other folks, they're already pretty much anchored, and the tax benefits can outweigh the downsides of incremental anchoring. Also, you can't get evicted...

I bought a house and moved out several months after purchasing it for health reasons. The house was an anchor, that I also feel held me back.

I had to take a number of jobs with higher pay, that weren't beneficial to my career. Almost every decision was can I pay for this house as well.

Outside of my special use case. It's an anchor point in your life. I like this job but it's further away from my house. I like this job but it's in another city. Etc.

You lose optionality when you commit your capital to an illiquid investment. That is, you no longer have the option to spend money on things which may have a higher ROI. Any type of commitment loses optionality.

Update: this is a great podcast episode on using optionality to your advantage (http://investorfieldguide.com/wolfe/)

Being able to seize opportunities (that require relocation) when the chance comes, perhaps? A house can become a boat anchor in those instances.

Probably mobility, hence increased ability to seize opportunities as they present.