The objective of the game is to catch the Darkfriends, not to save the Lightsiders. Not lynching gives us one less chance of doing that, at no benefit in longevity for the town.

For example, suppose that out of fifteen players we have 5 Darkfriends (or assorted scum.) The starting ratio of Lightsiders vs Darkfriends is 10-5. Now, assuming one night kill every night, here's how many attempts we have to catch a Darkfriend:

Numbers go as follow: Lightsiders-Darkfriends (lynch attempts made)

Day 1 lynch / Day 1 no-lynch
Day 1: 10-5 (0) / 10-5 (0)
Day 2: 8-5 (1) / 9-5 (0)
Day 3: 6-5 (2) (ly-lo) / 7-5 (1)
Day 4: 4-5 (3, lost) / 5-5 (2) (lost)

So you see, a no lynch doesn't gain us any additional time, while it actually loses us one attempt to lynch the Darkfriends.

Or what if we have six Darkfriends?

Day 1 lynch / Day 1 no-lynch
Day 1: 9-6 (0) / 9-6 (0)
Day 2: 7-6 (1, lylo) / 8-6 (0)
Day 3: 5-6 (2, lost) / 7-5 (1, lost)

Same results.

Four Darkfriends?

Day 1 lynch / Day 1 no-lynch
Day 1: 11-4 (0) / 11-4 (0)
Day 2: 9-4 (1) / 10-4 (0)
Day 3: 7-4 (2) / 8-4 (1)
Day 4: 5-4 (3, ly-lo) / 6-4 (2)
Day 5: 3-4 (4, lost) / 4-4 (3, lost)

Same results.

Let's try it with five Darkfriends and a serial killer. Chances to get a Darkfriend.

Day 1 lynch / Day 1 no-lynch
Day 1: 9-5-1 (0) / 9-5-1 (0)
Day 2: 7-5-1 (1) / 8-5-1 (0)
Day 3: 5-5-1 (2, ly-lo) / 6-5-1 (1)
Day 4: 3-5-1 (3, lost) / 4-5-1 (2, lost)

Same results.

Now let's add that the serial killer also kills a Lightsider each night.

Day 1 lynch / Day 1 no-lynch
Day 1: 9-5-1 (0) / 9-5-1 (0)
Day 2: 6-5-1 (1) / 7-5-1 (0)
Day 3: 3-5-1 (2, lost) / 4-5-1 (1, lost)

Same results.

Essentially, with odd no-lynch gives us no advantage, but saves the Darkfriends from one of their risks. With even numbers, no lynch gives nothing, but does not cost a lynch attempt either. But it's still a bad idea subjectively.

That was the objective part.

Now, the other reason we need to lynch, is because lynches give evidence. I don't think there has been a single Lightsider lynch thus far that has not included Darkfriend participation. So even if we do lynch a Lightsider, that allows us to narrow the scope of investigation. It also removes one of the decoys the Darkfriends get to hide behind. The number of Lightsiders in the early game is a disadvantage for us, it basically confuses the Light's investigation and allows the Darkfriends to hide in the crowd.

A day 1 no-lynch saves the Darkfriends' cover while depriving us of the information that would allow us to narrow the scope of investigation. Like shooting ourselves in both feet with a single bullet.

And with the objective detriment I pointed out at the beginning, that's three serious disadvantages for a no-lynch, compared to zero advantages.