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I have travelled for very little money in the past, hitchhiking my way around, sleeping behind gas stations or in nature, or utilizing sites like Couchsurfing where people can host you for free (in exchange for cultural exchange). I've crossed all of Europe and into the Balkans this way, as well as went up and around the western states in the US. While I realize this isn't the most fun way to travel for many (but for me it is!), travelling is still doable on a very low budget if you know how to travel and prioritize the concept of travel before your own comfort. I've done a lot of regular backpacking as well. Of course, the situation complicates itself if you're from the US, have a family, lots of student loans or health care debt to pay off, and have very little PTO. In Sweden at least, as with many other countries in Europe, we have a minimum of 5 weeks PTO. And either way, it's customary for people between high school and university to go on a gap year travelling the world.
With some proper budgeting and staying at hostels, or doing things like Worldpackers where you volunteer at hostels for room and sometimes food, you can travel the world for $10-15k per year easily. If you only do half a year or whatever, it's really not that much money if you prioritize travelling and saving up before other stuff. For some it might still be a lot of money, but it must cost something if you want to go for such a length of time. Otherwise you'll just have to become a busker and a vagabond, hitchhiking around. Australia even has a working holiday-visa for 1-3 years up til the age of 31 that is very popular for people to go on, where people work odd jobs in agriculture and what not, often with accommodation included and very good pay (even if the work can be tough), which then is used to continue travelling.
For the guy in the video, biking around is quite cheap compared to flying and whatnot. If you're camping by yourself, your only expense is food, if you've done off with all the other obligations in life like rent and loans. This means you can do it very, very cheap as well. I don't know his situation, but he probably sold off everything else, gave up his place or rented it out. Travelling that way inherently means some risk-taking. And for many people it's worth it.
I've seldom met travellers with a trust fund. And I don't have a trust fund myself, nor have received loads of money from parents to fund my travels. This is just such a bullshit answer that always pops up.