Question: I just read that physical changes are temporary and reversible while chemical changes are permanent and irreversible. If that is the case, why are some chemical reactions reversible. Does it mean that chemical changes are reversible?

Answer: 
The statement you challenge is a gross oversimplification and generalisation that fails to capture much of the subtlety of chemical reactions.

It seems to be pitched at describing the difference between simple examples such as the melting of water (physical, easily reversible by putting the water in a freezer) and the simple reaction between chlorine and hydrogen to give common salt (chemical, not spontaneously reversible or dinner tables would be far more entertaining).

But the variety of possible chemical reactions is far bigger than that. Many chemical transformations can be reversed easily given the right conditions. Esterification, the reaction of an acid with an alcohol, makes new molecules and water, for example. But to push the reaction to produce the ester, chemists need to remove the water or the reverse reaction just undoes the new bonds. So they have a cool piece of equipment called a [Dean-Stark apparatus][1] that removes water from the reaction to ensure they get the product they want. The whole point of this is a recognition that the underlying reaction is *reversible* and needs to be pushed in one direction.

The key to reversible reactions is that there is some *mechanism* that can undo the new bonds created in a chemical change. In many cases there is no such mechanism which makes many chemical changes impossible to reverse, which is why a simplistic view might distinguish physical from chemical change. But this is unfair on the variety of chemical behaviours.

Another example where you might expect reversibility is the conversion of diamond to graphite. Graphite is more stable under normal conditions but the conversion is not seen. This is because the *mechanism* to convert diamond t graphite would need to break a very large number of chemical bonds in diamond (every carbon connected to other carbons in an infinite tetrahedral grid) to get graphite (every carbon connected to 3 other carbons in an infinite hexagonal array using delocalised multiple bonds). At very high temperatures and pressures (such as carbon dissolved in liquid iron at pressure) many of the bonds in any form of carbon are already broken and the two forms of carbon can interconvert (this is roughly how diamond is formed in nature and laboratories). The reason why reversibility is not normally seen is that, at room temperature, there is no available mechanism to break the bonds.

Sometimes reversibility has tragic real-world consequences. Thalidomide is a chiral molecule one form of which is a mild sedative and is active against some diseases and cancers. The other form is a dangerous teratogen, causing monstrous deformities in the fetus. Unfortunately there is a reaction path in living systems that interconverts the two isomers, hence tragedy for pregnant women.

In short, reversibility is sometimes possible in chemical reactions, *if* there is an easily accessible *mechanism* to undo a chemical reaction under the right conditions. It is wrong to say that *all* chemical reactions are irreversible.

[1]: [https://en.wikipedia.org/wiki/Dean%E2%80%93Stark\_apparatus#:~:text=The%20Dean%E2%80%93Stark%20apparatus%2C%20Dean,other%20liquid](https://en.wikipedia.org/wiki/Dean%E2%80%93Stark_apparatus#:%7E:text=The%20Dean%E2%80%93Stark%20apparatus%2C%20Dean,other%20liquid))%20from%20a%20reactor.
All chemical reactions are reversible. But the back reaction may be extremely improbable. For exemple the combustion of hydrocarbons produces $\ce{CO2}$ and $\ce{H2O}$. But if you mix and heat a mixture of these two gases, you will never even obtain one molecule of any hydrocarbon by the back reaction, because the equilibrium constant is rather huge. The reaction seems irreversible.