These are the following reason why a cake might turn out dry
1. Substitutions:

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There is a reason why certain ingredients are used in a recipe. If you have made a substitution try to use only an alternative that does the same function as the original ingredient.

2. Room Temperature Ingredients:

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Unless otherwise specified in the recipe, try to use room temperature ingredients while making the batter to help in even baking.

3. Over mixing:

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One of the biggest reasons for a dry end result is due to over mixing or over beating the batter. Mixing just until combined and at times just folding the ingredients will help in making moist cakes.

4. Measuring Ingredients:

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Did you know that there is a difference in the weights of a sifted and unsifted flour? There is a technique to measuring flour properly failing which will topple the balance between the wet and dry ingredients making your cake drier. See How to Measure Flour properly in Baking

5. Oven temperature:

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Buying an Oven thermometer is one of the best investments to make if you are an avid baker. It helps to understand your oven especially since not all ovens work equally.

Also see:
1. Tips to Successful Egg Substitution
2. How to find out the role/purpose of eggs in a recipe?
3. 7 Most Common Mistakes in Baking
4. Baking Substitutes 101