High-grading involves harvesting the biggest and the best trees. This is attractive because it is most profitable, but it is also attractive because it is easy to confuse it with selective cutting. Over time, high-grading is usually significantly more disruptive than a clear cut. The biggest trees are not always the most mature. On the contrary, the may well be the healthiest and best trees. By removing them, you are taking away the best and leaving the worst.
But you will rarely be criticized for high grading, since you will leave a forest intact. In fact, you might garner praise from urban environmentalists unfamiliar with high-grading.
See this link for reference.