Because poverty, in fact, is a vicious cycle.
Let's paint a more or less common scenario here: Say that you have a family living in poverty. How they ended up in poverty could vary from individual to individual. There are too many reasons to name, so let's just settle with them being in poverty. Say the family has a few children. The parents must now work to give them food and shelter, paycheck to paycheck. This leaves no money in excess for the parents to store for the child's future. This also leaves no money for them to have luxuries. The child most likely goes to a bad school in a bad neighborhood and is most likely surrounded by bad influences. Now that we have a scenario down, let's examine how that's going to keep a poor person from escaping poverty.
1. The only priority of the parents is to have the basic needs met. Maslow's hierarchy of needs states that, individuals won't pursue other needs if the basic needs are not met. Your top priority is ALWAYS the basic needs. If you're struggling to have those needs met, you aren't going to think about things beyond them.
2. Poverty mentally leads the adults into frustration. This makes them take bad decisions, for example alcoholism and drug use to help them escape the situation, or domestic violence to vent out their frustration. These things are huge obstacles to moving up the social ladder.
3. So the job they hold isn't great. It pays low and doesn't require any experience. Jobs like these are unstable. The adult is at risk of losing their job. If they lose their job, they're plummeted deeper into poverty. Why don't they get better jobs? Think about it this way... better jobs require education; education takes time. Time isn't something a struggling parent who's trying to make ends meet has, once again, this takes us back to meeting basic needs as a priority.This can be even harder on a single parent. What if they try to force the time out? well if they do that, they could be facing homelessness or sick children. You aren't going to worry about education in times like that, no matter how beneficial it might be in the long run; you just can't afford it.
Do you see how this is going to repeat itself?
Now let's go back to the children..
The children should have a fresh start, they have education and should utilize it to their success, right? Wrong. Poverty is working against them from the time they're born. The keys to a child's success are: Health, Nutrition, Education, and Support. Poverty literally takes a stab at all of these.
Health: Luckily, in America, all children have free health care until they're 18. However, their parents do not. Poor health in a mother's pregnancy will pass over to her child and can effect him for life, or at least, through childhood. If a child has poor health, he is more likely to have interruptions with daily life, school included.
Nutrition: Poor families usually can't afford to eat well. Healthy food is expensive; trashy food is dirt cheap. So a child who lives in poverty is either 1. Not getting enough to eat 2. Getting trashy food to eat. A child who goes to school hungry or malnourished isn't going to do well. in the long run, not doing well in school isn't going to get you into a university, and it sure as heck ain't gonna make you smart enough to earn a full-ride scholarship. So that debunks the whole "work hard in school and get into college through scholarships" myth. And as a bonus, I'll throw in that a majority of full-ride scholarships are given to athletes. However, a poor child most likely isnt involved heavily in sports because they can't get to the sports practices and events and can't afford the gear anyway, so that possibility is tossed out as well. Doing poorly in school is also going to hurt the child's self-esteem and self-efficacy.
Support: A child has to believe that they're worth something. This can be hard for them to imagine when they see their living conditions. Because of frustration and lack of education, a parents might not help in giving the child the self-worth they need to experience. Quite the opposite, the parent may demotivate them. They can hardly find support at school, most of their teachers are taught not to rock the boat, and most of them don't care to, anyway. Also a lot of teachers who most likely come from the middle class, don't understand the living conditions of their students. They often become frustrated with both the child and the parent. So they're no help. What about their peers? This is where it gets fun... a poor child isn't likely to be accepted by their better off peers. They might have unkempt appearances and are unable to follow social trends which isolate them from their peers' living experiences and social circles. So now their peers aren't going to give them support either. Not the good kids, anyway. But you know who is? the "bad" peers. These are their peers which often live under similar conditions or have at least known the same conditions, but have figured out a way to have what others have in not so good ways. I'm talking about gangs. Gangs often form as alliances of minorities who aren't getting what they need from society, and so decide to take it from it one way or another. With a gang, this poor, isolated child is offered acceptance into a "family" (I'm sure you've heard gangs use that term.) and friends. They're also offered ways to get luxury goods and money (by illegal means). Do you see why a gang would be tempting to a child living in these conditions?
By the early adult years, you now have a child who hasn't gotten any of the keys to success, so how are they going to get out of poverty? They're going to repeat the cycle, as their own parents most likely did.
In order for a the cycle of poverty to be broken, most people need an outside force, someone who isn't in the cycle, but very understanding. Adults can look to community resources, they honestly help. (however, it's hard to do this when a lack of education might mean they don't even know such resources exist, and when society is giving them a cold shoulder for looking towards these resources.)
A child can break the cycle by becoming strongly resilient, this too requires the help of a person who can help the child's self-esteem or by playing a strong role model that they child can aspire after. This isn't as easy as it sounds, I can't stress that enough.
Sorry for the super long answer, but you had a super complicated question.
I'm not gonna take the time to call out some of these horrible and badly answers, but you should know that most of the people answering are coming from a different walk of life and have no merit in sociological or political perspective.