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Yeah, I learned on a TRS-80, a C-128D, and finally a PC. But, times have changed and they've done so in many marvelous ways I'll cover in a second.
But first, remember what BASIC is: Beginners All purpose Symbolic Instruction Code. Comparing it to an expert's language like C++ is at the very least foolishness. It was designed to teach programming.
And back to modern programming. Most new students learn from something like Visual Basic (GUI-based high-level application development), or by 'modding' their video games (these all run high-level scripting languages, usually imperative and object-oriented), or by acting as a sysadmin for their Linux box, eventually hacking the scripts enough to get the idea. Sadly, that usually ends down a dirty road of Perl and PHP...
BASIC did let you hack away at a terminal and get output. But that entire model, however simple we may fondly remember it to be, is fairly worthless now. Object Oriented Programming's here for good reason, and students learn programming easer in this way.
Considering that almost all the apps we run today are event-driven and object oriented, from the desktop to the web, it makes sense to start there. Writing an event handler for a button on a VB form or creating new instances of health kits or weapons in a video game make great entry points into programming --- without the implicit masochism of terminal hacking.
But if you really want to do it old-school, get Spirit or ANTLR and write your own interpreter.