Never make absolute statements (contradiction in terms intended)
There are times when trade-in can make sense, look into how long it might take to sell, how much you would get for it, how badly the dealer wants to make the sale this month, etc.
I have purchased 6 cars directly from a dealer (3 used, 3 new). In 3 of those cases (2 new, 1 used) I was actually better off trading in. Once was due to the time frame involved. The next was due to having a car that just wouldn't sell privately used (tried for 3 months with LOTS of different types of advertising), the dealer was able to re-sell it for $2000 more than they gave me, which was itself $1000 more than I was trying to sell it for privately. The final case was a real lemon of a used car that the dealer thought they could do something with anyway, they gave me considerably more than it was worth (really just meant a larger discount off the sticker on the new car) and were never able to re-sell it.
Of the remaining used cars I have turned over, all but one I sold privately and did quite well with, that final one was donated to a local church for one of their employees.
SY / LSS / Touring / Hardtop