You need to first be able to understand your parents concerns and why they don't want guinea pigs. Then consider what you can do to alleviate those concerns.
Is it a cost thing? My Donald is 3 years old and has already had two lots of complicated surgery and a couple of UTI's. The first surgery set me back £300, the next £919. Plus visits to my regular vets either side and we're already looking at around £1500 in the two years I've had him. Obviously there are things you can do such as getting a job of your own and starting to build a savings fund to pay for these kind of costs. Are you working at the moment?
I agree with
@Lady Kelly .
Try to understand where your parents come from and then try to address the sticking points.
- companionship: healthy guinea pigs live 5-7 years on average. A single guinea pig relies fully on you for round the clock stimulation and interaction throughout the whole time as you have to replace all its social needs.
But what when you are busy studying, have an active social life, fall in love or move out into accommodation you cannot take your piggy with you? That is a long time to plan ahead.
- financing. If you are in the US, Canada or Australia medical cost are even higher than in the UK. That even goes for euthanasia in order to spare your piggy a very painful slow death - and you the pain of having to watch helplessly.
General vets are much cheaper (with operations in the range of $150-300, but often have no or very little experience with guinea pigs so there is a higher risk of post-op recovery and complications), a life saving operation by an exotics vet can set you back US $1000 upfront.
PS: For price comparison purposes: UK £1 is about US £1.30 or Cdn$1.75 and Aus $1.85
Vet bills, when they occur, are the single most expensive headache in any pet's life. Since there is not much (and nothing at all in the US/Canada or Australia) in the way of pet insurance for guinea pigs, this means that you need to save up on a weekly basis right from the start.
If your parents are struggling to pay/save up for human illness, as many people in the US do, then it is entirely understandable that to have these amounts of money accessible at all times just for a pet are a problem. Unlike in the UK where there is a pet charity to help with vet cost for people on benefits and where vet clinics allow payment plans, there is nothing comparable in other countries.
Sadly because guinea pigs are so cheap to buy and are considered short-lived children's or teenager's pets that is not worth spending money on, we are regularly bombarded with posts from teenagers with very ill/dying piggies looking for a last minute miracle cure because their legal guardians refuse to pay any medical cost. It is always an upsetting experience, especially when it is an easily preventable or curable illness with a good recovery rate in the early stages.
- space: guinea pigs are ground roamers and not climbers. They really need all the space they can get to stay healthy and to solve any disputes that rise along the way. Guinea pigs are a lot like people: in cramped conditions disputes are much more common. The biggest reasons why teenage boars fight is because they are kept in too small cages where they cannot get away from each other as they normally would. Do you have the space for a large cage that you can divide if necessary and are you willing to poo patrol a cage daily and change it twice weekly to keep it from smelling for the next 5-7 years whatever else happens with your life?
These are questions that are important to address before you get a pet and vital to solve with your parents so all the sticking points and responsibilities are clear for everybody. It is vital not just for the pets, but also you as a family as you do not want to end up with a huge row that sours your relationship for a long time. We see on here the emotional fall-out all too often when this has not happened. And it is generally at the cost of a guinea pig's life.
Children And Guinea Pigs - A Guide For Parents
PS: I agree that the link above does contain misleading or plain wrong information. If members want to link in outside resources, please make sure that they comply with welfare standards.
PS2: I have yesterday afternoon just spent £120 (ca. $160) for a consultation and medication for a 1 year old guinea pig with a not life threatening but rather painful long term medical issue that requires daily medication. You can just never predict whether you are lucky or not when you get pets....
We are by no means rich people on here; we have to plan carefully around our pets. I have had to cut back a lot on going out and spending on other interests or more expensive clothing to pay for my piggies as my main hobby, for instance.