Simple answer is Jupiter doesn’t have enough mass to fuse hydrogen into helium.
But you didn’t come here for the simple answer!
This process of turning hydrogen into helium is known as nuclear fusion and it is the energy source that powers the sun and most other stars. What drives nuclear fusion? For nuclei to fuse, they must be brought together at incredibly high temperatures and pressures. A celestial body needs to have enough mass to provide high temperatures and pressures like this. To put Jupiter’s mass into context, our sun is an example of a typical star and Jupiter’s mass is one thousandth the mass of our sun. In other words, to turn Jupiter into a star like the sun, you would have to add about 1,000 times the mass of Jupiter!
But what about low mass stars?
Low mass stars are low in mass in terms of stars! For example, OGLE-TR-122b weighs one-eleventh of the mass of the Sun; it is only 16% larger than Jupiter but it is still 96 times as massive as this giant planet! Low mass stars are very interesting because their interiors have much in common with gas giants but as we can see it all comes back to mass.
Why is Jupiter sometimes known as a failed star?
Although Jupiter has a long way to go in terms of mass, it does have some interesting similarities with our Sun. The two objects are very compositionally similar. By mass, the Sun is 71% hydrogen and 27 % helium with traces of other elements and Jupiter is about 73 % hydrogen and 27% helium. If we are to look at composition only, our local star and the biggest planet in our solar system are almost identical! It is for this reason that Jupiter is sometimes called a failed star.
Stars and planets are created in two very different ways. In a nutshell, stars are formed from massive clouds of dust and gas called nebulae. As the mass grows, the core of the baby star is squeezed tight together and grows very hot. It becomes so compressed and hot, the core ignites, and the process of nuclear fusion begins. Gravity pulls smaller amounts of dust and gas together and this forms planets around the star. So, Jupiter has a similar composition to the Sun not because it was a failed star but because it was born from the same cloud of gas that gave birth to the Sun.