1. I LOVE the relentless acceleration the DCT offers - no loss of forward momentum with gear changes. Puts a huge smile on my face every time.
2. I LOVE that the car is never unsettled during shifts. Those with track experience, especially racing or at least with a stopwatch involved, will recognize the supreme value of smooth driving and not unnecessarily unsettling the weight shifts of the car. Now it is true that if one is really good at using a MT, especially heel/toe downshifting, this can be accomplished without a DCT, but the DCT is perfectly consistent, while no human is. Having become very very good at driving a MT and doing it smoothly while driving as fast as I can on a track, I actually marvel at how incredibly well the DCT does this. For example, the track I practice on actually gets slow enough to permit me to downshift into first gear on the last turn before the straight-away, which is something virtually nobody does in their MTs (and which some have wrecked their MTs trying because of letting the clutch out too early), and that provides a significant advantage.
3. Better fuel economy. If the M3 is your daily driver, this helps with a little of the guilt of driving this gas guzzler. I can enjoy the advantages of the DCT effortlessly shifting for optimal economy, and then, with the flip of a paddle, get all the aggression out of the engine that I want.
4. Best of both worlds. If engaging the clutch yourself is orgasmic to you, this won't mean much, but if not, then the loss of engaging the clutch yourself may be more or less offset by the convenience of having an automatic in the right situations. At the same time, you're not going to be taking any hits in performance when you want to drive aggressively or on the track.
5. If I wanted a raw sportscar experience, I wouldn't be getting an M3. From my perspective, the DCT suites the whole M3 experience well. This is a sedan/coupe that is engineered to be sporty and not a purpose-built sportscar from the ground up. Its my daily driver including sole winter car. It comfortably sits 4 adults, conveniently accepts front and read facing child seats, and is loaded with noise insulation, heavy features, a relatively high ctr of gravity, and too much technology getting in the way of steering-feel, etc. A DCT is a very reasonable option in a car that is supposed to be a jack-of-all trades, IMO. Would you get a MT in your mini-van? If yes, then the DCT is definitely not for you. If not, then this line of reasoning may appeal to you in some way.