The first issue of X-Men introduced seven main characters who appear in X-Men comics to this day, some of which have become icons of pop culture. The second issue introduces The Vanisher.
The comic opens with the X-Men in costume in Westchester. They seem neither hated nor feared - Angel is mobbed by local fangirls and Cyclops is celebrated for saving some people from a falling wall (by disintegrating it into smaller chunks and dust). But another evil mutant has arisen! This one, with the ability to teleport and calling himself the Vanisher, has outwitted security staff to rob a bank, and then demanded a figure of TEN MILLION DOLLARS! from the government lest he steal some secret files. This is still early for superhuman activity in the 616 - although he shows up as a costumed villain, they don't seem to realise he probably has powers. The X-Men are locally well-regarded in Westchester, and their fame has apparently spread nationally since the first issue - Xavier borrows an aircraft from the government's "Department of Special Affairs" and has a contact in the White House.
Xavier has been monitoring the situation, and sends in the X-Men, who are soundly defeated by the malicious mutant. Professor X joins them in person for a second attempt, and ultimately uses his mind-control powers to gain the upper hand - specifically by mindwiping the Vanisher. This is troubling, even within context, as is the implication that Xavier sent the X-Men against the Vanisher to fail. The Danger Room scenes - and even the name - imply that Xavier's attitude to training is that there should be real jeopardy. It's easy to see where the later retcons will fit.