Well, there are a few different aspects to consider in these discussions:
1) Cash flow - from a cash-flow viewpoint, paying off the house makes sense, because it reduces monthly payments and makes living on one income feasible. This is a valid point for people considering having children, or for people concerned about the stability of one person's job.
2) Investment standpoint - yes, the market may return higher rates, but it's not really fair to compare paying off a mortgage (pretty safe return on your money, especially if you plan to stay put and therefore are not really affected by any fluctuations in the value of the house. Also, I believe somebody here said Canadian mortgages are not fixed for 30 years, but for a shorter term (like maybe 7 years?). In that case, getting it paid off before interest rates rise has value. It is true that sinking all your money into real estate, if you don't have other savings, may not be wise. And I don't think this couple has a big enough emergency fund (I'd prefer to see 6-12 mos expenses). Still, once the house is paid off, you can weather a lot of financial storms, like:
3) Crashes - during the most recent financial crash, in the U.S., people who had kept large mortgages on their homes in favor of stock investing, were doubly screwed. Their investments tanked, they lost their jobs, and their houses were underwater, all at the same time. Many people lost their homes to foreclosure because they didn't have enough savings left to ride out the storm, or because they had to move to find work and couldn't sell their home for what they owed. A paid-off house would have significantly softened the impact of that crash on many people (i.e., if your house was paid, you could probably live on unemployment until the crisis was over, and let your stocks rise back up without having to sell at the bottom). There's definitely some value to this, especially in an over-valued market like Canada (where housing prices never did crash, I think they inevitably will at some point.)