There are many engineering factors that determine g ratings. The cumulative fatigue damage from dominant operations primarily determine g-ratings. When landing, this contributes heavy fatigue positive g's. When flying, the natural forces of gravity and turbulence (to include gusting winds) contribute to fatigue damage. These stresses are felt throughout the control systems. Therefore, the plane is engineered to be stronger in all its considerations to support and counter the greater fatigue concerns.
http://adg.stanford.edu/aa241/structures/structuraldesign.html
How come V-n diagrams are not symmetric?
V-n Diagrams tend to visually reflect some of the more dominant fatigue considerations. Engineered considerations that influence g ratings also are reflected in the V-n Diagrams for similar reasons. Notice the sharp changes in shape in the following Vn diagram and its explanations:
http://adg.stanford.edu/aa241/structures/vn.html
So why not strengthen everything to have higher g limits? Cost and useful return on investment. There is little practicality to have an aircraft stressed to +/- 100 g's if it has little useful load, is too heavy to fly, or costs so much very few customers can afford buying it and pay for its operation.
Balances in weight, cost, strength... are in constant flux throughout design to provide an overall useful and affordable aircraft. Equal g ratings is not a priority, however, meeting regulatory minimums is a priority.
https://www.faa.gov/about/office_org/headquarters_offices/avs/offices/air/directorates_field/small_airplanes/media/CPS_Part_23.pdf
There are normal and abnormal conditions in which an airplane is stressed for negative g's.
Normal negative g's include: in-flight turbulence, recovery from a bounced landing, down drafts / wind shear ... and other engineered limits that are reflected in negative g ratings.
Abnormal negative g's include: walking on or otherwise loading the top of a wing, unrated aerobatics, excessive snow loading while parked, excessive pilot induced control moments causing negative g's, excessive road bumps while in transport ...
Conditions violating negative g design considerations include: improperly secured or excessively worn folding wing hardware, worn or warped wing gusset or related fastening hardware, fatigued or weak weldments, corrosion ...
G-ratings have to do with Damage Tolerance
As a point of reference. Fatigue failures are usually more significant at gross weight, and therefore utility and ultimate g ratings (regulatory) are usually given at gross weight.
Strength of Materials is a particular area of science and engineering that characterizes properties of materials, including fatigue. Computer simulations can run thousands of tests using variations in parameters to anticipate fatigue failures before they actually occur in flying aircraft.
An aircraft can be engineered to have greater negative g limits than positive g limits; however the cost for this non-useful engineered feature would likely be unacceptable to customers. Lower useful weight to have the higher negative g support structure as an example.
How come planes can endure more positive than negative g's?
However, the FAA over many years of experience has set standards for minimum g ratings to help control accident outcomes.
As an example, see Part 25 AIRWORTHINESS STANDARDS: TRANSPORT CATEGORY AIRPLANES
Subpart C--Structure Fatigue Evaluation
Sec. 25.571
Damage-tolerance and fatigue evaluation of structure.
http://lessonslearned.faa.gov/Comet1/25.571.pdf
and an A/P's insights under the following debrief:
https://www.faasafety.gov/files/gslac/library/documents/2011/Jul/55585/FLYING%20LESSONS%20110623.pdf
In terms of engineering to meet regulatory requirements, the cumulative probability of fatigue failure resulting from negative g's is less than the cumulative probabilities of fatigue failure from positive g's. The design limits reflect these failures through probability equations relating likeliness to occur and level of impact.
FAA SYSTEM SAFETY ANALYSIS AND ASSESSMENT (acceptable methods)
http://www.faa.gov/documentLibrary/media/Advisory_Circular/AC%2023.1309-1E.pdf
Methods of working probability equations:
http://people.qatar.tamu.edu/shehab.ahmed/ecen_459/Lec34-37.pdf
The information provided in these links are to show the effort involved is no small task for aircraft designers. Many thousands of failure modes accumulate when every part, joint, human error, environmental, and every other factor potentially part of a failure is considered.
So when asking a designer what the effect would be on g-rating based on a specific failure mode of a part, is not a reasonable question to ask because of the extensive interactions with the total system to be considered.