Do you have any suggestions for tiny districts where there is just one person in an area to be reduced? There is no difference between talking about the area to be reduced and the person to be reduced, and the community members find the board discussions as you describe disingenuous.
School boards should make their decisions based on the programs that students need to succeed. When you throw in the discussions about the qualifications of the 'person' or whether they are well liked, etc. then it does not meet the test of making decisions based on the best educational program for students.
The board does not know and should not know, whether that teacher has other qualifications/licenses/seniority that will keep the individual employed, although in another position. Those things that decide who is layed off and who is bumped, are spelled out in and controlled by your labor agreements.
We don't know that any one individual teacher will stay another year, leave to take a better position or get run over by a truck on the way to the grocery store next week. Discussions considering positions/individuals, even if we keep it to the 'position' almost always veer into areas that cause legal liability for the district.
Recent example: Very small district with a high school agriculture program (consisting of one class and an after school FFA club) taught by a well loved but relatively new teacher (who also taught science and math); and the board and superintendent were considering cutting the program. The community assumed that ending the program meant losing the well loved teacher, and keeping the program meant keeping her. So it turned into a public discussion of her personal characteristics and qualifications. The board listened to the public and directed the superintendent to keep the program. The community expected that the teacher would remain. In addition the budget called for laying off one or more high school teachers. Lo and behold a more senior (less well loved) science teacher was licensed to teach agriculture as well. The current agriculture teacher, with only a few year’s seniority, was slated to be laid off. This resulted in total chaos, public meetings where things were (allegedly) thrown, the board over-ruled the superintendent and the union agreement, and ordered the newer teacher re-instated. Flash forward to a lawsuit, money costs to a tiny district, ultimately the superintendent and the high school principal left the district in frustration. Now add the cost of a superintendent search.
You can explain to the public why the board will only discuss programs, and yes your board understands this impacts individuals and you empathize with this. However the negotiated labor agreements dictate who ultimately will be laid off and you as a board must construct an educational program that is the best you possibly can under the current budget climate, without using individuals and their qualifications to make those decisions.
If you have enough money in your budget to afford the cost to the district of talking about and using individual qualifications/positions in making these decisions, then you have enough money not to make the cuts. Let the public talk about the person, but not at the meeting. Explain to them why you can't do that without endangering the district. And then stand your ground, in the best interest of the district and students.