Error org.lwjgl.LWJGL Exception
When the launcher tries to run Minecraft, you get a crash report that starts with: "org.lwjgl.LWJGLException: Could not create context". This is most commonly caused by an antivirus program or firewall mistakenly blocking some of the installation files.
Temporarily disable your antivirus program and firewall, download Minecraft once again and choose "repair" if prompted to do so, then try logging in.
If that doesn't fix the problem try to remove/uninstall Minecraft and download files again.