The two questions inherent in any decision to purchase an insurance plan is, "how likely am I to need it?", and "what's the worst case scenario if I don't have it?". The actuary that works for the insurance company is asking these same questions from the other end (with the second question thus being "what would we be expected to have to pay out for a claim"), using a lot of data about you and people like you to arrive at an answer.
It really boils down to little more than a bet between you and the insurance company, and like any casino, the insurer has a house edge. The question is whether you think you'll beat that edge; if you're more likely than the insurer thinks you are to have to file a claim, then additional insurance is a good bet.
So, the reasons you might decide against getting umbrella insurance include:
Your everyday liability is low - Most people don't live in an environment where the "normal" insurance they carry won't pay for their occasional mistakes or acts of God. The scariest one for most is a car accident, but when you think of all the mistakes that have to be made by both sides in order for you to burn through the average policy's liability limits and still be ruined for life, you start feeling better.
For instance, in Texas, minimum insurance coverage levels are 50/100/50; assuming neither party is hurt but the car is a total loss, your insurer will pay the fair market value of the car up to $50,000. That's a really nice car, to have a curbside value of 50 grand; remember that most cars take an initial hit of up to 25% of their sticker value and a first year depreciation of up to 50%. That 50 grand would cover an $80k Porsche 911 or top-end Lexus ES, and the owner of that car, in the U.S. at least, cannot sue to recover replacement value; his damages are only the fair market value of the car (plus medical, lost wages, etc, which are covered under your two personal injury liability buckets). If that's a problem, it's the other guy's job to buy his own supplemental insurance, such as gap insurance which covers the remaining payoff balance of a loan or lease above total loss value.
Beyond that level, up into the supercars like the Bentleys, Ferraris, A-Ms, Rollses, Bugattis etc, the drivers of these cars know full well that they will never get the blue book value of the car from you or your insurer, and take steps to protect their investment. The guys who sell these cars also know this, and so they don't sell these cars outright; they require buyers to sign "ownership contracts", and one of the stipulations of such a contract is that the buyer must maintain a gold-plated insurance policy on the car. That's usually not the only stipulation; The total yearly cost to own a Bugatti Veyron, according to some estimates, is around $300,000, of which insurance is only 10%; the other 90% is obligatory routine maintenance including a $50,000 tire replacement every 10,000 miles, obligatory yearly detailing at $10k, fuel costs (that's a 16.4-liter engine under that hood; the car requires high-octane and only gets 3 mpg city, 8 highway), and secure parking and storage (the moguls in Lower Manhattan who own one of these could expect to pay almost as much just for the parking space as for the car, with a monthly service contract payment to boot).
You don't have a lot to lose - You can't get blood from a turnip. Bankruptcy laws typically prevent creditors from taking things you need to live or do your job, including your home, your car, wardrobe, etc. For someone just starting out, that may be all you have. It could still be bad for you, but comparing that to, say, a small business owner with a net worth in the millions who's found liable for a slip and fall in his store, there's a lot more to be lost in the latter case, and in a hurry. For the same reason, litigious people and their legal representation look for deep pockets who can pay big sums quickly instead of $100 a month for the rest of their life, and so very few lawyers will target you as an individual unless you're the only one to blame (rare) or their client insists on making it personal.
Most of your liability is already covered, one way or the other - When something happens to someone else in your home, your homeowner's policy includes a personal liability rider. The first two "buckets" of state-mandated auto liability insurance are for personal injury liability; the third is for property (car/house/signpost/mailbox). Health insurance covers your own emergency care, no matter who sent you to the ER, and life and AD&D insurance covers your own death or permanent disability no matter who caused it (depending on who's offering it; sometimes the AD&D rider is for your employer's benefit and only applies on the job).
99 times out of 100, people just want to be made whole when it's another Average Joe on the other side who caused them harm, and that's what "normal" insurance is designed to cover. It's fashionable to go after big business for big money when they do wrong (and big business knows this and spends a lot of money insuring against it), but when it's another little guy on the short end of the stick, rabidly pursuing them for everything they're worth is frowned on by society, and the lawyer virtually always walks away with the lion's share, so this strategy is self-defeating for those who choose it; no money and no friends.
Now, if you are the deep pockets that people look for when they get out of the hospital, then a PLP or other supplemental liability insurance is definitely in order. You now think (as you should) that you're more likely to be sued for more than your normal insurance will cover, and even if the insurance company thinks the same as you and will only offer a rather expensive policy, it becomes a rather easy decision of "lose a little every month" or "lose it all at once".