As Carol tells it, the Sagebrush area, situated at the western edge of La Cañada, is physically separated from the main part of the city. In the 19th century, the few kids of local ranchers would have found it much easier to go down the hill to Glendale schools.
As the larger area grew in last decades of the 19th century, a bridge was built over the Arroyo Seco that linked La Cañada to Pasadena. That meant the kids in La Cañada proper were closer to Pasadena's schools, and traveled there for their high school education (La Cañada had a primary school for the younger set). At this point, people in the Sagebrush area were already used to sending their kiddos to Glendale schools, and just continued to do so.
Additionally, though La Cañada formed its own unified school district in the early 1960s — an elementary school district predated this by several years — the city itself was not incorporated until 1976.
My guess is that there was some type of bond measure in the '60s to pay for La Cañada's high school, a bond people in the Sagebrush — at this point, firmly served by GUSD — may have either refused to pay or were explicitly excluded from. Remember, at that point, La Cañada was unincorporated county land, so parents in the Sagebrush might have thought it unwise to throw in their lot with a district with no city.
If there was grumbling about this arrangement, it did not appear to come to a head until 1991, when a group of parents filed a petition asking for the Sagebrush to be transferred to LCUSD. This sparked a 10-year legal battle, with the California State Board of Education ruling the area should stay with Glendale. Appeals filed after that decision went nowhere.
But this year, a group of Sagebrush residents restarted the issue, getting the La Cañada City Council to approve a resolution supporting the transfer of the area to LCUSD in June. The La Cañada school board followed suit in August.