Pushups certainly tear your muscles, just like any other sort of movement. The difference is that pushups are usually used for training endurance, whereas (weighted) dips are more of a strength movement (for some).
ANY movement can train for endurance, it depends on volume, intensity, and reps. That said, any movement can also be used for training strength. Have you ever done push-ups with a weighted vest? - That's strength training if you can only do a couple.
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The reason why Chris and Steven are annoyed is because people will come in asking a question and people will give them bad advice. They've been on this forum for years and have to deal with it day after day. So seriously guys. If you don't know FOR SURE that the advice you're giving is sound then go to eatmoveimprove.com and see if you can find anything on it there. If not then find some valid articles, read some books, look at some studies on pubmed. We offer fitness advice based on sound science.
It should be a requirement to have a good knowledge of physiology (high school level at least), and have read starting strength before being allowed to give advice.