What would be a thesis statement about advantages and disadvantages of euthanasia?

A thesis statement about the advantages and disadvantages of euthanasia might be something along the lines of: "One important disadvantage of euthanasia is its potential for abuse." 
Ideally, your thesis should occur in the first paragraph of your paper, following a brief introduction to the paper's topic that gives the reader a sense of the debate to which you will be contributing. In this case, you are writing about the pros and cons of euthanasia, otherwise known as assisted suicide. Supposing that you are writing a persuasive essay, your thesis statement should summarize the main point for which you will argue and describe, briefly, how you will go about defending it. 
When drafting your thesis, you should think not only about the claim you want to defend but also how you might support that claim. Make a list of the ideas you want to include in your essay and identify which are the strongest by thinking about whether they would be accepted by someone with an opposing point of view. Once you have narrowed your list, outline your paper by selecting one point for each paragraph. Two or three defending points is standard for an argumentative paper. 

The first thing to remember about a thesis statement is that it makes an argument. It is not a statement of fact. The goal of the rest of the paper is then to prove that argument.  I do not know what direction you intend to go with euthanasia as your topic, so my thesis statement help is going to be more general. 
More than any other thesis statement format, I recommend what I call the "point and counter-point" format. This format causes the statement to state something that you actually intend to disprove with your main argument. The formatting is straightforward.  Start with the word "although," and then state the argument that you disagree with.  The word "although" forces a dependent clause which needs to be followed up with an independent clause. That second clause is what carries your main argument.   This is an effective thesis style because you admit to readers that other opinions exist. You also discuss their validity; however, major paper portions are then devoted to presenting an even better argument.  Here is a possible thesis with euthanasia as the topic for discussion.
"Although proponents of euthanasia argue that it is a mercy to speed up the inevitable, this kind of thinking is flawed and euthanasia is still murder."
You might completely disagree with that thesis statement, but it is easily flipped around to make the opposite argument. That's the advantage to that format.