Because pressing control and left click in Minecraft on a Mac results in a right click, it is impossible to left click (and therefore break blocks or attack) whilst sprinting. Before you mark this as a duplicate of bug reports claiming that the control + left click = right click does NOT work, let me be perfectly clear : control + left click = right click DOES work on Mac, but the fact that this cannot be disabled prevents you from left clicking whilst, for instance, sprinting with control because it results in being a right click. So, here's my suggestion for a simple fix : in the controls panel of the options on the Minecraft Mac client, add the option to DISABLE the control + left click = right click for the people who do not need it and do not want it for the reasons stated above (because you can use a mouse or click with two fingers on a trackpad to right click anyways).
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CubeTheThird
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NO. PLEASE. READ. In 1.6 they added the fact that, SPECIFICALLY FOR THE MAC CLIENT, pressing control and left clicking right clicks! THIS IS INSIDE THE GAME. The feature was added because normally this does happen in the normal OS, but Mac disables this feature for games because many games, FPS for example, use the control key. Some people, not realizing that this conflicts with sprinting with control, requested that Minecraft add the feature to the game. BUT THIS FEATURE IS ABSOLUTELY OBNOXIOUS. Furthermore, the control + left click thing DOES NOT happen on Windows because IT WAS NOT ADDED IN 1.6. Please reopen this.
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Look. 1.6.2 changelog. Look at the 4th bulletpoint. It says it right there. It was added. Do you believe me now? https://mojang.com/2013/07/minecraft-1-6-2-pre-release/
CubeTheThird
Using MC-13695 as a reference. According to that old report, the game always used ctrl + left click = right click on Mac. When the LWJGL libraries updated, there was a bug where this functionality was broken, hence the report. The issue was later fixed when the updated libraries were included. The functionality you are looking for is not intended behaviour, and thus is a feature request. For feature suggestions or changes please do this on Minecraft Suggestions on Reddit.
I doubt the behaviour you are requesting would even be possible to implement. There is essentially no difference between the client on Mac, or any other OS, for one thing. The key behaviour you describe seems to be handled by the OS, so it's not likely simple to override it. Lastly, keyboard input is handled by the LWJGL libraries which Minecraft uses, so in order for it to be possible to do this, the functionality would have to be available in these.