I guess the author's argument is that, because of the frequent settlements, one needs to invest the mark-to-market gains and fund the losses. As the exchange traded futures contract is negatively correlated to interest rates, the mark-to-market gain happens when interest rates are low, so not a great time to invest, while the loss happens when interest rates are high, so not a great time to look for funding.
Over-the-counter (OTC) forward contract does not have to go through this pressure (even though these days some forms of initial margins, variation margins and collateralization - all of them needing to account for some funding/investing - are accompanying most OTC contracts).
Edit: In general, theoretically, there is an expectation that futures price is less than forward price, if the uknown amount (at expiry) is positively correlated to the (stochastic) discount factor.
Given $T$ expiry date and $S$ payment date and unknown ${\cal F}_T$-measurable amount $X$, $\beta_t = \exp (-\int_0^t r_udu)$ stochastic discount factor (its inverse, bank account value, being the standard numeraire here) and (zero-coupon) bond price $B(t,T)=\beta_t^{-1}\mathbf{E}[\beta_T | \cal{F}_t]$, we have:
$$ {\rm Fwd}_t^X = B(t,S)^{-1}\beta_t^{-1}\mathbf{E}_t[\beta_S X] $$
and, due to (continuous) resettlement (and other technical assumptions),
$$ {\rm Fut}_t^X = \mathbf{E}_t[X] $$
(making futures prices a martingale).
It can then be proved that the futures convexity correction is:
$${\rm Fut}_t^X = {\rm Fwd}_t^X - \beta_t^{-1} B(t,S)^{-1} \mathrm{Cov}_t(X, \beta_S). $$
Time $0$ relation is:
$${\rm Fut}_0^X = {\rm Fwd}_0^X - B(0,S)^{-1} \mathrm{Cov}(X, \beta_S). $$
In the Libor futures/forward price context above (long futures contract), the covariance is positive.
(Proofs are available in Hunt and Kennedy's book, Financial derivatives in Theory and Practice.)