soft-pedal
It’s the quiet pedal on a piano. Peddling is selling, which is the opposite of what you are doing.
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Wrong: Don’t soft peddle the numbers.
Right: Don’t soft-pedal the numbers.
It’s the pedal on the left. You’re playing it quieter.
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Wrong: He soft peddled the layoffs.
Right: He soft-pedaled the layoffs.
Peddle means to sell. He was doing the exact opposite.
Where it comes from
The piano. The soft pedal is the one on the left, and pressing it makes the instrument quieter and more muted. To soft-pedal something is to play it down—the same gesture, applied to bad news.
Why the wrong one survives
Because peddle is a real word and soft sell is a real technique, so soft peddle turns up sounding like ordinary business vocabulary.
It is the reverse of what you mean. Peddling is pushing a thing at someone until they take it. Soft-pedaling is making the thing smaller so nobody looks at it directly.
The same trap catches backpedal, which gets written as back-peddle for exactly the same reason. Both of those are feet, not sales.
In fairness
Keep the hyphen when it is a verb—soft-pedal the announcement. And in American English the past tense is soft-pedaled, one L.
No point soft peddling it.