Take, for instance, the establishment in Heller of the right to bear arms as an individual right. Most conservatives believed that to be the case all along, and think it is clear from the wording. However liberal observers were more likely to notice that this interpretation had not appeared in 2 centuries of jurisprudence, and societies of professional historians had long reached the opposite conclusion about original intent.

For another, look at Citizens United which established that corporations had a right to free speech, and therefore could not be restricted from spending on political speech. Conservatives saw this as a straightforward issue of, "I have no actual freedom of speech if I cannot spend money to broadcast it." Liberals noted that this overturned several previous precedents, and the Constitution had never intended corporations to be considered people.

In these and other cases, conservatives don't recognize the creativity of interpretation because the result seems natural and right to them. Liberals do notice.

The same is true going the other way. But liberals do not object to noticing that they have been creative, so are less likely to fail to notice when they have been.