We aren't really reliant on Canadian timber. The US produces more board-feet of timber than any other country in the world[1], and most of it is used domestically.
If we were dependent on Canadian timber, we probably wouldn't be exporting the exact same lumber to them[1]. They're our largest importer of lumber.
The simpler explanation is that we have (or had) a free trade agreement with Canada, and it's just plain cheaper for all parties to import or export when/where the supply chain is already present.
It could be a distribution cost issue. It could be cheaper to use Canadian lumber in some parts of the US than it is to transport US lumber from where it is sourced to where it is needed.
There are also regional specializations. Like, BC has a substantial amount of Western Red Cedar which the north western states can’t meet the demand for alone.
We also send raw materials to be processed by mills in the USA. This isn’t as common as it once was. Then we also send lumber which US mills process. Some examples would be fir boards would are turned into flooring, window sash, stair treads, etc. BC produces a ton of material like this which is fodder for all kinds of mills, large and small. We try to keep that business here, but we tend to mostly dimension raw materials for export, rather than actually mill them and add any meaningful value.
We import a lot of hardwood lumbers from the USA. I’ve personally bought and milled American hardwoods for furniture in my home. We have beautiful hardwoods in Canada, but there are a lot in the USA we simply don’t grow, or at least not commercially.
There’s also the phenomenon of intra-industry trade. One big example is natural gas, which the US exports to Canada and Mexico, while paradoxically importing natural gas from Canada.
Beef and pork are another example I can think of though, this has to do with specific cuts and quality for various markets.
[1]: https://www.eworldtrade.com/blog/top-10-wood-producing-count...