If you have Adobe Acrobat DC Pro, you can create a custom command using the following JavaScript code to delete all even numbered pages:
// process document from the last page to the first page
for (var i = this.numPages-1; i>=0; i--) {
if (i % 2) { // this will delete all even numbered pages
this.deletePages(i);
}
}
To learn about how you can create a custom command, follow the steps here: Create Custom Commands in Adobe Acrobat DC Pro - KHKonsulting LLC
If you want to delete all odd numbered pages, just change line #3 to this:
if (!(i % 2)) { // this will delete all odd numbered pages
If you are using an earlier version of Acrobat Pro, you can use an Action to accomplish the same. If you are using Adobe Acrobat Standard, you don't have access to the action wizard or custom commands, and you would have to write a folder level script to create a new menu item that can delete odd or even numbered pages.