Well, the most important reason is that God tells us so in the Bible. The clearest declaration of this is found in 2 Corinthians 6: 14-16
Do not be unequally yoked with unbelievers. For what partnership has righteousness with lawlessness? Or what fellowship has light with darkness? What accord has Christ with Belial ? Or what portion does a believer share with an unbeliever? What agreement has the temple of God with idols? For we are the temple of the living God…
2 Corinthians 6: 14-16
As Christians, it is important that we honour God, and the only way of doing that is to obey what He teaches us in the Bible. The consequences of not obeying Him can be huge; the ramifications splinter into every aspect of life.
Impact on the core of your life.
If you are a Christian your identity is found in Christ . You are being shaped after the image of God and your priority is God. If you marry a non-Christian, whether they are of another faith or none at all, it means that they do not share the most important part of your life. However sympathetic they seem to you, they cannot understand the joys or sorrows that you will have in your Christian life, nor can you effectively share these with them. However close you now seem, there will always be a tension between light and darkness, since you will not be able to walk the same path together before God and share the same love for Him. Even though there may be many areas of practical compatibility, e.g. hobbies or a desire to set up a home, because your core values are different, there is a potential for growing further apart.
Impact on how you live your life and raise your children.
Of course, if there is already a conflict with the core part of who you are, this will extend to other parts of your life. One simple example of that is how you will live your day to day lives as a family. Will you have family worship together? Will you attend church together? Will you be able to raise your children in the way of the Lord as you will want to?  . Will you be able to agree on moral boundaries? How can you do that if you are being constantly undermined or even opposed by the example of your husband or wife?
Train up a child in the way he should go; even when he is old he shall not depart from it.
Lead away from, rather than to, God.
You miss the benefit of encouraging and strengthening one another to a God-honouring life , and being able to fellowship with one another while striving for the same thing. You may think that you can lead them to the Lord, but that isn’t a reason to marry them. You may want to evangelise them, but you should not use a marriage or romantic relationship as a tool for that. The reality is that it can be hard to say “no” to something you want, but sometimes it is the wisest and best thing to do. Sometimes there needs to be a short-term struggle at the beginning to avoid a long-term struggle in the future.
- ‘Belial’ – A Hebrew word meaning worthless, later translated devil in Jewish and Christian texts.
- Colossians 3:1 “Since, then, you have been raised with Christ, set your hearts on things above, where Christ is, seated at the right hand of God.”
- Proverbs 22:6 “Train up a child in the way he should go; even when he is old he shall not depart from it.”
- Ephesians 6:4 “Fathers, do not provoke your children to anger, but bring them up in the discipline and instruction of the Lord.”
- Proverbs 27:17 “Iron sharpens iron, and one man sharpens another”