Nope, sure doesn't seem to be a good picture.
You've brought up two incidents, the 2009 guitar, and this 2017 problem with a rabbit...on an airline that carried 95 million people last year.
95 million customers last year - hundreds of millions of customer contacts between reservation agents, gate agents, flight attendants and pilots every year, which add up to billions of customer contacts that clearly happened between these two incidents.
So, your two data points, out of billions, aren't really telling the whole story then, are they?
Most of the Guardian article was about the forceful removal of Dr. Dao, not the rabbit, which tells me that the journalists at the Guardian are looking to sell a few papers while the social-media fueled outrage remains fresh.
I'll provide a couple of more data points about United, so that you, and the rest of BITOG who don't fly much, have never been on United, and are forming your opinion based on few facts, can make a more informed judgement...unless you wanted to just bash United, which seems to be the sport de jour these days....and in which case, you don't really care about making an informed judgement.
I'll start with a couple of United "firsts", not all of them, we don't have space, but a few, so you can get a better idea of the company: flight attendants, the first in the industry, were a United innovation in 1930. United was the first airline to adopt flight simulators, in 1954. First to operate the Boeing 767. Launch customer for the 777 and United pilots worked with Boeing to help design the airplane. First to fly airplanes directly over the North Pole from US to Asia. First commercial aviation flight on biofuel. First Major airline to go paperless in the cockpit. We were first to use aircraft radar and a whole host of other innovations, but I'll move on to today...
Pets: United does more than any other airline to ensure the safety of pets. The 767-300/400 that transported this rabbit, all have heated bulk cargo compartments, so that the pets stay warm during the flight. We generally keep it between 62 and 68F. Pets are transported in vans and the vans stay on the ramp, with the pet in climate controlled conditions, until the last minute when they're boarded. I've had dogs, cats, birds, lizards, even cows (a calf, actually) in my airplane. When they're on my airplane, I usually take the time to find the owner and let them know that their pet is safely on board. With a picture if I'm able to do it. The cow didn't have an owner, it was being shipped to a buyer...
Other airlines put pets on the baggage carts and drag them around the ramp, so that they get the full exposure to the heat/noise/cold of the ramp conditions. I see it all the time in airports: pets on baggage carts. There are no statistics on pet deaths, but United carries a lot more pets than other airlines, so we take extra care with pets. We instituted our "Pet Safe" program in 2010.
Fantasy Flights: in 1992, United partnered with Make a Wish foundation to offer "Fantasy Flights". United provided airplanes and gates, free of charge, and United employees volunteered their time. Now, every year, in early December, at every major airport served by United, Cleveland, Chicago, LAX, SFO, IAD, IAH, DEN, and others, Children who are terminally ill board a United airplane, and the airplane takes off. It returns to the same airport, but to a different gate that's been decorated as the North Pole. The different gate is staffed by United employees (the same ones that have been continually bashed on this forum and in the news now for three weeks as uncaring) dressed as Elves - and the airplane full of terminally ill children gets to meet Santa at the North Pole. That airplane took off, flew (for just a few minutes) and they are magically transported to the North Pole.
Pearl Harbor Survivors: On December 6th of this past year, United Airlines flew, for FREE, every Pearl Harbor Survivor, and their families, in First Class, to Honolulu for the 75th anniversary commemoration of Pearl Harbor. I was honored to shake the hand of a Battle Ship Gunnery Chief who I met in DIA as I was going to work. We chatted on the train. I was in the presence of a hero, and United flew every one of those heroes to Pearl Harbor.
Disabled Vets: For two decades, we have helped those warriors take to the slopes of Aspen, Colorado, for the National Disabled Veterans Winter Sports Clinic, a week-long event established by the U.S. Department of Veterans Affairs (VA) to give soldiers with serious injuries a place to experience skiing, rock climbing, snowmobiling, sled hockey and snowshoeing. We flew over 500 vets to Colorado for this event this year. We block seats a YEAR in advance, so that wheelchair and other disabilities can be accommodated.
US Olympic Team: We transported the entire US Olympic Team to Rio this year. We've been an Olympic sponsor and the official transport of TEAM USA since the 80s. We safely carried everything from kayaks, to track and field equipment like pole-vaulting poles, and skis, to Olympic games all over the world. We accommodate all kinds of gear to make sure TEAM USA is ready to compete.
https://hub.united.com/united-transporting-team-usa-equipment-1975172339.html
Performance: United's performance in all of the DOT metrics: cancellations, delays, mishandled bags have improved dramatically in the past few years as the merger has been accomplished. Involuntary denied boardings now are half what they were a few years ago, not that the news reports that. Mishandled bags is dramatically lower.
For example: SWA arrived on time 78.7 % of the time while bumping 1.08 out of 10,000 passengers. United arrived on time 78.2% of the time while bumping 0.77 out of 10,000 passengers. The top airline in on time was Virgin America at 79.9% on time. All of the top airlines are fiercely competitive for on time performance, but the bump statistics are interesting, in light of the Dr. Dao incident.
We get positive customer feedback every day. Our Mileage Plus loyalty program (another industry first, by the way) is consistently ranked as the best. So is our app. We've partnered with Saks 5th Avenue for our First Class service and celebrity chefs for our food. You're focused on a couple of news stories White Wolf, but I encourage you to come try our airline. We have the best route structure of any airline in the world, seriously, the best, and our competitors know it, and we can get you anywhere you want to go on this planet.