Why were linesmen re-named assistant referees?

Introduction
In 1891 linesmen were introduced to decide when the ball whether the ball was in or out of play and to indicate throw-ins, goal-kicks and corner-kicks. This role has changed drastically throughout the years but the biggest change came in 1996 when they were given the duty of indicating whether a player in an offside position and had committed an offense.
The Switch
In that same year linesmen (lineswomen) and linesman (lineswoman) were re-named to assistant referee and assistant referees. The revision later came into effect in '97. In an amendment to the proposed new text submitted by FIFA it states the reason for changing linesmen to assistant referee is as follows:
"The word 'linesmen' does not accurately reflect the tasks of the linesmen who are, in actual fact, assistants to the referee"
FIFA stressed the growing duties and evolvement of the role which weighed in heavily on the name change.
The IFAB stated this was done "to reflect their important role and to recognize the growing number of female officials" which was also a major factor after the 1995 FIFA Women's World Cup held in Sweden which saw an increased use of female officials. Notably among those female referees in Sweden was Catherine Leann Hepburn who was the first American woman named on the FIFA list.
FIFA Badge
With the name change also came a change to the Linesman FIFA badge which was introduced some time in the early 1990s but abandoned in the late 1990s.

Later came the introduction of the FIFA Assistant Referee badge which can be seen below.

The term 'linesmen' or ‘lino’ is still used often today but unofficially.
Conclusion
The reason for the change from 'linesmen' to 'assistant referee' was caused by an evolution in the role and the need for using a gender neutral term ratified in the 1996 IFAB Annual General Meeting with FIFA and several other national football associations.
Sources:
HOW FOOTBALL HAS CHANGED 'LINESMEN' to 'ASSISTANT REFEREES' | The IFAB Assistant referee (association football) | Wikipedia When were on-field match officials introduced in football? | The IFAB The fourth official for the inaugural Rapids home game in 1996 | MLS Referee Stats Women World Cup 1995 Sweden » Referees | World Football FIFA WORLD CUP APPOINTMENTS | US Soccer Referee Program Why was linesman changed to assistant referee? | Big Soccer 1996 Minutes of the Annual General Meeting of IFAB | IFAB Referee badge: UEFA vs FIFA | Refereeing World