Depending on the time, when I open a website and do a traceroute, I notice that website goes to a different path than the usual, and some websites just never open. Why the same network alternate between two very different paths (different ISP/countries) for the same website?
Is it traffic on one path so it switched to another even if it wasn't reliable?
Professional grade websites are typically served via a content delivery network, CDN, whereby the files/data are served from several mirrored servers across the globe. Your request to that URL/website address resolves to the server (IP address) closest to you.
If you don't physically move, you should be hitting the same IP address (resources) every time / every day.
It is possible that your network provider is jacked up. For example, I've been to a large corporation where my Internet was routed out 3000 miles away from me and across time zones. As a result, lots of Web application layer stuff breaks such as default Map views, calendar invite times (timezone issues), etc.
Traceroute can be a useful tool on your network, where you can compare the results to what is expected. On the public Internet, it can give you a completely different path than what actual data may take. Your traffic may pass through multiple ISPs, any or all of which can look for and redirect ICMP and traceroute in order to disguise their internal networks.
Your traceroute may be purposely routed over a backup or other path. It is also possible that there is some load balancing or instability happening with one ISP. You simply cannot know, and your actual web traffic may take a much better path than what you are seeing.
