There are two ways of answering the question about whether children spread coronavirus.
One is to look at virus levels in children. The guardian study linked above indicates that children do carry a viral load similar to adults. This would seem t indicate that children could pass it on, just as adult do and so shouldn't be treated differently.
The other is to look at known coronavirus cases, and to examine whether there are any patterns to indicate that children have been active in spreading the disease. For example, have teachers and childcare workers been over represented in cases, or have any schools become clusters of the disease. Evidence acted on by the Swiss and Dutch governments seems to suggest that children have not active spreaders, and so children could be excluded from rules around social distancing for example.
I prefer as an evidence source the second method - I prefer evidence based on occurred fact rather than theory - but I understand others would prefer the first.
Ultimately its extremely unlikely that children cannot pass on the virus at all, but evidence does seem strong that they are much less active spreaders than adults.
The relaxation of restrictions on them, therefore, becomes one of appetite for risk. How much of a priority do you make equal access to education which can only come from fully reopening schools; how much increased risk can you ask teachers to take on; do you prioritise other areas of the economy over children's education; how can you communicate this message with a nervous teacher and parent population? Not easy questions.