As a matter of fact, Catholics do not teach that Christians should pray to saints. What they do teach is that we should ask for saints' intercession.
In the case of Catholic prayer "to saints," Catholics ask saints or a particular saint to pray on their behalf. They might say "Please pray for my roommate whose lung has collapsed. I know that you are in heaven with Jesus, and so I ask that you pray to him for me." The common response to this is, why not pray to Jesus Himself? Why not go directly to the source? Why are intermediaries needed, when the Bible says there is no mediator between God and man?
To answer these questions, let's consider the process of intercession. In most evangelical churches, there are prayer chains, prayer partners, and intercessory prayer teams. These people are responsible for listening to the prayer needs and concerns of the congregation, telling these concerns to others if necessary, and praying for these concerns. To give an example of this in action, when my roommate's lung collapsed, I asked my mom to pray for her. My mom, in turn, asked her Bible study to pray. This is an example of intercession. When I asked my mom to pray, I was not praying to her; rather, I was asking her to pray on my behalf. Why not go straight to God? Because I wanted more people praying for my roommate. Because I wanted the support of my faith community, the Church. Because I coveted the prayers of godly people. I was not asking for a mediator between myself and God; rather, I wanted someone to walk alongside me in prayer. The only difference between this familiar process and Catholics who pray to saints is that those saints are dead.
The next problem is precisely that: if the saints are dead, how can they hear us?
First, consider the resurrection. Those saints are not dead, but risen. We believe that Christ rose from the grave, killing death for all the saints. The promise of resurrection is the promise of life.
However, one may believe in the resurrection and believe that those in heaven must be happy, otherwise what use is heaven? Hearing our prayer requests would burden them, making Heaven an unhappy place. Doesn't this contradict the teaching that the saints are glorified?
Not quite. In the book of Revelation, the saints express many emotions, but impatience features more prominently than happiness. In Revelations 6:10, the martyrs cried "Oh sovereign Lord, holy and true, how long before you will judge and avenge our blood on those who dwell on the earth?" In other places the prayers of the saints are thrown to the earth by angels in a golden censor. Moreover, in the parable of Lazarus and the rich man, Lazarus looks into hell and sees the rich man suffering and hears his petitions to save his family from hell (Luke 16:19-31). While this parable is likely meant to be taken symbolically, there is no assumption that those in heaven are completely oblivious of earth or hell.
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