Without knowing more, sounds like your logger might be "high grading" you, that is, taking the valuable trees and leaving you with trash. The logger argues, "If we just take some of those big ones so the little ones underneath can grow, you will have a better woods." That argument normally is bunk, unless planned with a forester and practicing good silviculture. If the understory is not good now, it likely always will be bad. Generally, what grows well now on a site is pretty good evidence as to what should grow on that sight in the future, from a forestry perspective. But a local consulting or DNR forester will know more about your location.
I find it hard to believe large white pines are junk and have no value where you live. White pine makes beautiful furniture, table tops, trim and architectural lumber. From one our trees we got 18" wide boards, which I put down as flooring in our bedroom, using square head nails. Not a single board has split, warped, etc. When people see this, they ask in amazement, "where did you get that flooring?" Local carpenters buy white pine from me for their construction work. I also supply a local cabinet shop based on its needs.
Nine years ago a big white pine broke off in a windstorm about 36' feet up. That tree provided the 18" boards I mentioned. All told, we got over 1000 board feet of lumber from a single tree, and white pine lumber, rough sawn, I can sell usually for $1.25 - $1.40 a board foot -- that's more than $1,225.00 for lumber from a SINGLE tree. What's your logger paying you for the white pine he wants to take? Obviously, you won't get "finished" prices, but take note of the value of white pine.
Some of the large branches make very interesting character lumber, and if not, all of the branches 2" and larger make great firewood. They all end up in the gasifier that heats my shop.
White pine is a classic tree from the northeast extending west to Minnesota. It is the tree that built many of the homes and other buildings in huge parts of the east and into Nebraska and Kansas. It grows fast, typically lives up to about 350 years, but is subject to wind and storm damage, and blister rust fungus is tough on white pine.
Don't proceed to cut the white pine before you educate yourself on its present and future value.