How is defying multiple subpoenas not obstruction?

Subpoenas can be, and often are, challenged. If they're challenged, the courts ultimately have to decide on the merits of the challenge. If the challenge is rejected, it doesn't mean the recipient can be charged with obstruction. But if recipient refuses to comply with the court's order directing compliance with the subpoena, that could be pursued as obstruction.

Could the witness's reject the subpoena? Then away to the courts we go again?

In fact, many have been--whatever administration and Congress you look at, there you go. (D) or (R), either side of the Congress or the president.

Often you hear the phrase "we've complied with all subpoenas," and that's often a misleading truth. It's a staple in most administrations.

Often a house of Congress will say what they want and, if things aren't too rancorous, the subpoena will have been crafted to meet both side's requirements--ruling out extra stuff, including just what's requested. All the subpoenas were complied with (because that was negotiated ahead of time).

If things are more rancorous, the subpoena will be challenged outside of court, they'll work out a compromise, the old one withdrawn and a new one produced. All the subpoenas (that remained valid) were complied with.

And if the two sides are deep into rancor the courts will be asked to arbitrate--and they usually just tell both sides to work it out on their own. Even then, as long as it's in court, administrations will say that all the valid subpoenas were complied with (but it's an open question as to whether some were valid, so those don't count).