One argument Muslims use for Islam is that it is the world's fastest growing religion. This is one of those arguments that I don't really feel I should have to refute, but since people actually use it, it must be done.
The first problem with this argument is that it isn't necessarily true that Islam is the fastest growing religion. It's just that it is the fastest growing identified religion. Human beings, being human, first of all do not always class religions as religions. Evolution, for example, is a religion, yet it is not officially recognised as such. How fast is this religion growing? Who knows? Furthermore, all religions typically start off small. When a new religion starts, it obviously doesn't make the official statistics, because no one's ever heard of it. Yet, if it starts with one person, and they convert one person, that's a 100% growth rate in a single second, far more than is even possible for Islam to reach. And that's just one person converting one person.
But an even bigger problem is that growth, in and of itself, is insufficient to establish truth. In fact, the speed at which contradictory religions grow tends to fluctuate. There was a time, long before Islam even existed, when Christianity spread like wildfire. It was the fastest growing religion, and one day, may be so again. Yet, Muslims do not change their religion to reflect the growth rates. The irony here is that if growth rates were a convincing argument, they would become a self-fulfilling prophecy.
The real question that must be asked is why Islam is growing so fast. The truth is, Islam actually has a low conversion rate, and a high apostasy rate. Islam is growing mainly because Muslim women tend to have more children, mainly because Islam, especially in countries dominated by its laws, provides few opportunities for them to do anything else. When a Muslim couple have a baby, that baby is automatically counted as a Muslim, and in some countries, it's even illegal for them to convert. Therefore, as Muslims tend to have more children than other faiths, Islam grows faster. If we limited records to only professions of faith/lack thereof, Islam would probably be the world's fastest shrinking religion.
In order to make a coherent case for one's religion, one must have valid reasons for why it is true. Islam, of course, is not true. In fact, because the Qur'an affirms the Bible while simultaneously contradicting it, Islam must necessarily be false. Therefore, the argument from Islam's growth rate means nothing.
A better argument would be if Allah had actually shown up at some point in history, but whereas Muhammad kept making excuses for why he could not perform a single miracle, Jesus is actually the only God who ever walked the earth. He performed many miracles during His life, up to and including His own resurrection. Since a mere human cannot rise from the dead, Jesus' resurrection demonstrates His Godhood.
But it actually does more than that. See, Jesus' death wasn't an accident. Rather, He died to receive the punishment we deserve for our sins. Because He took the wrath of God, we don't have to. All it takes is to repent of our sins, confess Jesus as Lord, and believe He rose from the dead. Doing that results in salvation. After that, get baptised as a show of good conscience towards God, and be joined to a local body of believers.