That's the easy part. We can mostly agree that SEL matters; in fact, we ought to agree that it already happens in classrooms. It's impossible to avoid; where children are around adults, SEL is going on. Asking if SEL should occur in a classroom is like asking if breathing should happen in the room. The real question is whether or not it should occur in a formal, structured, instructed and assessed manner. That is the question that starts all the arguments. We can break down the arguments by asking the same questions we ask about any content we want to bring into the classroom.
Why do we want to teach this?
Some SEL proponents have developed a utilitarian focus. Summarizing the work of the Aspen Institute National Commission on Social, Emotional and Academic Development, EdWeek said "social-emotional learning strategies center on research that has linked the development of skills like building healthy peer relationships and responsible decision making to success inside and outside the classroom." But what happens if we approach what used to be called character education with the idea that it's useful for getting ahead? Doesn't SEL need to be about more than learning to act like a good person in order to get a grade, a job, and a fatter paycheck? Are you even developing good character if your purpose for developing that character is to grab some benefits for yourself?
If we're going to adopt SEL in order to essentially teach students to be better people, then who will decide what "better" looks like? Is "tolerance" going to be one of the virtues, and if so, does that mean that students must learn to tolerate persons who would not be tolerated by their families (be that married gay folks or strict religious conservatives)? Should students be taught to feel empathy for everyone, from Nazis to sociopaths?
The Collaborative for Academic, Social and Emotional Learning (CASEL) identifies five "competencies" for SEL(self-awareness, self-management, responsible decision-making, social awareness, relationships skills). That framework is widely used, but "explained" with a wide variety of definitions (one resource says it includes "achieving useful goals"). All of them are heavily loaded with value judgments; how many arguments have you been in your life about whether or not something was a "responsible" decision or not? Who decides if a goal is "useful?"
We have been down this exact road before. In the 90s, Outcome Based Education was going to be a great new thing in education, but before it could gain traction, a bunch of folks noticed that it included an element of teaching values, and a large number of parents were certain that was not a job they wanted the schools to do. OBE never recovered. As two articles in this packet from AEI note, much of what comes under the SEL umbrella used to be considered the providence--indeed, the whole point--of religious and faith-based education.
Wherever SEL is implemented, expect a huge fight over what will actually be taught.
How will we teach it?
How exactly does one design a unit to teach a room full of children to empathize or be self-aware?
Google "SEL Resources" and page after page of links will pop up. Software companies that are plugging their "personalized learning" packages are selling SEL elements to be included, evoking the picture of a child being taught about emotions and character by a computer.
SEL learning occurs in the wild through unplanned, unprepared moments of opportunity. One of my toddler children fell last weekend, requiring an ER visit and stitches. He's fine, but he now understands and uses the word "sad." It was an effective SEL moment, but not one I'd want to deliberately manufacture for other children. Can the teachable moment about human emotions, empathy, or self-awareness be formally constructed?
How will we assess it?
How exactly do we measure these social and emotional qualities? What would be a good test of empathy or self-awareness? Plenty of folks are working on the problem, but their solutions require some hefty suspension of disbelief. NWEA, for instance, scored a grant for their technique of reading students' social-emotional qualities based on how long the student waits to click the answer for an on-line multiple choice test. Software has been field-tested for reading student emotions via facial expressions. Just this May, the news came out that Amazon is working to teach Alexa to read the emotions in your voice.
These kinds of software solutions could be used to assess student social and emotional behavior against a desired outcome. But who decides what the "correct" answer is on such assessments? And how easy will it to be to game such a system? We're talking about assessments that try to read student emotions--will we teach students to feel those emotions, or teach them how to act like they feel those emotions? We don't have a way to truly measure empathy, which means we'll have to judge students on how well they perform the appearance of empathy.
What will we do with the results?
What we can measure with software we can store with software, so as with all the other current assessments, the question becomes how will the data be stored and who will have access? Will future employers be weeding out prospects whose fourth grade empathy scores were too low? How much privacy is going to be violated, and how badly?
Does SEL Belong?
There is no question that SEL is important in education. Virtually every "How a teacher changed my life story" has a strong SEL element (though there is also ample evidence from business and politics that a lack of empathy, self-awareness, and responsible decision-making need not be an obstacle to success). The real question is whether or not SEL can be incorporated as a structured, formal, assessed element of education, and that question does not yet have a clear affirmative answer.