In one sense, your teacher is correct. *Right now*, the COM is outside the sun. It's been outside since around 2006- mid-Oct, and will stay outside until about 2010 mid-March. But the center of mass is definitely not always outside of the Sun.
If all the planets were all aligned on the same side of the Sun, the combined center of mass would lie about 500,000 km above the Sun's surface. But if Jupiter and Saturn are on opposite sides of the sun, the COM is inside the Sun.
In fact, from 2000-Jan-1 to 2100-Dec-31, the COM is inside the sun 37% of the time, and outside about 63% of the time. For the distance center-of-sun to COM, the maximum is 1.98 solar radius, the minimum is 0.134 solar radius, and the average is 1.165 solar radius. These distances are 682,187 km above, 602,595 km below, and 115,047 km above the surface, respectively.
Note: these numbers are approximate, because I ran the ephemeris program for 30-day intervals. A cycle takes about 200 months (16.7 years), so one data point every 30 days should be good enough for most purposes.
The JPL ephemeris is pretty much the state of the art. It includes the effects of the asteroids, as well as the planets and Pluto. But that only makes a difference of a few kilometers.
I hope that when you wrote "center of the universe", you really meant "center of the solar system". Planets don't have "weight", they're in free-fall orbits. They have mass.
As the planets move, they do NOT change the COM. They orbit around the COM. That's why the COM is such a good origin for planetary orbit calculations. (The COM does move in space, as the solar system orbits in the galaxy. But this motion does not have any "wiggles" in it as the planets and Sun orbit around the COM.)
Also, a small note about the 'AU' unit. It is no longer defined as the average Earth - Sun distance. It is just a plain distance, defined in kilometers. The problem with the old 'average' definition was, average over what time period? If it's a year, then which year?
[And I didn't even get to mention effects of General Relativity, so I will mention it here. The JPL ephemeris does include GR effects.]