So imagine this:
Euthanasia laws have passed. They're still quite strict, you must be quite elderly or have health conditions that won't let you live more than another 2-3 years.
At first, some people choose euthanasia options, while others choose to live as long as possible, hoping to be there for the milestones of their children and grandchildren, or just not go gentle into that good night.
All is well.
Then, a social campaigner notices: a huge percent of lifetime medical costs for most people happens in their final year of life. The NHS is already quite strapped for cash. With so many young and working people needing faster and better healthcare access, it can only be concluded that spending a large amount of money to ensure that grandma can spend one last Christmas at home is really a generational wealth transfer from young people to old people. Quite simple, really.
Then, the pressure begins to mount. It's environmentally unfriendly to try to stick around, you know. Old people simply cost more to keep going. Much like you see with women who have 4+ children now, you'd get all the comments on those who chose to prolong their lives: "a bit selfish, isn't she?"
And it would be "she," by the way. This will disproportionately impact women, because women are by far the more common spouse in a heterosexual marriage to outlive the other--many men will refuse to avail themselves of it until their quality of life is truly in decline because their spouse wants and needs them close, but women are more likely to be widows living alone. Women are expected to give more up, and to take on more burdens for others. We are the ones who live longer and we don't drop dead of sudden heart attacks as often as men do, so we cost more.
This is the scenario when we confine it to elderly and very ill people. If we allow euthanasia for intractable depression, as some countries do, all you must really do in order to exercise population control over unpopular groups is depress them with poor circumstances, then wait for them to volunteer. Or push them into it, and tell the world they volunteered.