The lineage of the National Hockey League, which played its first season in 1917/18, is normally tracked back through time as follows:
National Hockey Association (1909/10 to 1916/17)
Eastern Canadian (Amateur) Hockey Association (1905/06 to 1908/09)
Canadian Amateur Hockey League (1899/00 to 1904/05)
Amateur Hockey Association of Canada (1886/87 to 1898/99)
And this is certainly true, in the sense that these are the highest-quality hockey leagues in Canada in their times. They are the "major" leagues, meant in a sense different from the modern one.
However, if you want to track direct lineages of league-season to league-season, this progression isn't accurate. The AHAC led directly to the CAHL, which led directly to the EC(A)HA. But the NHL did not descend directly from the ECHA.
Before the 1909/10 ECHA season, the new owners of the mighty Montreal
Wanderers desired to move the team from the Montreal Arena to the
smaller Jubilee Rink. The three other teams in the league (Montreal Shamrocks, Ottawa
Senators and Quebec Bulldogs) strenuously objected to the move, finally
going as far as leaving the ECHA over the dispute. These three teams
formed the Canadian Hockey Association (CHA), accompanied by a new team
organized by Art Ross (All-Montreal), and the French-Canadian Montreal
Nationale, which had played in the rival Federal Amateur Hockey League years before.
The Wanderers, for their part, joined the new National Hockey Association, along with the Renfrew club from the Federal Hockey League, and Cobalt and Haileybury from the Temiskaming Mines professional league. A new French-Canadian club was created for Montreal, the Canadiens, to fill out the league. Every club in the league, save Wanderers, were owned by Ambrose O'Brien, the son of a wealthy mining magnate.
It seems clear to me, then, that the direct lineage that began with the AHAC in 1886/87 came to an end when the CHA folded early in the 1909/10 season. The CHA had hockey history on its side (especially since the Wanderers did not even originate as part of the lineage), but the NHA had Ambrose O'Brien's mining money. In the end, the cash won out. Some talk of a merger took place, but ultimately the NHA accepted the Ottawa Senators and Montreal Shamrocks into its fold, bringing to an end the line of the AHAC. Although the NHA featured two clubs with long histories in the lineage, they had come over from another league, their own having died.
In fact, the Montreal Canadiens franchise was offered to the owners of le Nationale by O'Brien, who turned it down. It could very easily have been the Montreal Nationals in the NHA rather than the Canadiens. There's some alternate history for you.