How come planes can endure more positive than negative g's? I.e. how come V-n diagrams are not symmetric?
The lines start at zero load factor because with no speed there is no lift. If you move further right, the upper line is determined by the maximum lift, while the lower line is determined by the minimum lift. Both have the same value only for symmetric airfoils - regular airfoils are optimized for creating lift in only one direction.

The upper and lower maximum load factor limits of the v-n-diagram are mostly determined by maximum gust loads in level flight, and in this condition they are represented by lines emanating from +1 g, such that the distance from +1 g in terms of positive and negative load factors should be the same. Add to this that your wings will create approximately 50% more force until they reach their maximum lift as compared to the minimum ( = maximum negative) lift (the details depend on the airfoil, of course), and then your load factor limits will be 1 + 1.5$\cdot$gust load factor in positive and 1 - gust load factor in negative direction.

For an example I have uploaded the polar of a supercritical airfoil which I calculated years ago with Mark Drela's ISES. It's the best I could find quickly - most polars only show the positive maximum lift, not the limit at the opposite end.



As you can see, the maximum $c_L$ is +1.3, while the minimum $c_L$ is only -0.8.

Let's look at a practical case: Utility category airplanes must be certified for +3.8 gs and -1 g. In level flight a positive vertical gust (updraft) might add +2.8 g. The same gust strength in negative direction (downdraft) will cause a load change of only -1.9 g (because the wing will stall earlier), which, when added to the regular 1 g at level flight will translate into a -0.9 g load factor. Close enough for limiting the negative load factor at -1 g.

At higher speed the gust will not stall the airfoil in either direction, and now we can simply assume that a gust will produce a positive load of 1 + gust load factor and a negative load of 1 - gust load factor. Let the gust load factor be 2.8, and your limits will be +3.8g and -1.8g, like in your example at 150 kts.

So far, I have looked at the rationale behind the load limits for certification. But also in real life there is a difference between positive and negative load factors: The wing spar has to carry the bending moment due to lift minus the wing weight. If it would need to carry the same aerodynamic loads in both directions (up and down), the wing weight would reduce the total positive load, but would make the total negative load greater. This is why the structure cannot endure the same load factors in both directions: You need to give the wing some margin to carry its own weight in addition to the aerodynamic loads.

Things look differently if you take the v-n-diagram of aerobatic category airplanes. Now you cannot readily assume that the plane will only fly straight, but you need to assume that it will be hit by a gust while flying upside down. Add to this that the symmetric airfoil will create the same lift in both directions before it stalls, and your envelope needs to be limited at ±6 g, making the envelope symmetric.